(************** Content-type: application/mathematica ************** Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 841102, 13685]*) (*NotebookOutlinePosition[ 842030, 13718]*) (* CellTagsIndexPosition[ 841939, 13712]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Arithmetic", "Title", TextAlignment->Center], Cell[CellGroupData[{ Cell[BoxData[ \(\(\[ExponentialE]\^\(\[ExponentialE]\^\(2 k\ \[Pi]\ \ \[ImaginaryI]\)\)\)\^\(\[ExponentialE]\^\(-\[ExponentialE]\^\(2 k\ \[Pi]\ \ \[ImaginaryI]\)\)\) /. \ k \[Rule] 1/3\ // N\)], "Input"], Cell[BoxData[ \(\(\(0.030953557167613194`\)\(\[InvisibleSpace]\)\) + 1.7392241043091323`\ \[ImaginaryI]\)], "Output"] }, Open ]], 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Rational[ 191, 24], Rational[ -2861, 240]}, 0, 13, 1]]], "Output"], Cell[BoxData[ InterpretationBox[ RowBox[{ "1", "+", "\[Epsilon]", "+", \(\[Epsilon]\^2\), "+", \(\(3\ \[Epsilon]\^3\)\/2\), "+", \(\(7\ \[Epsilon]\^4\)\/3\), "+", \(4\ \[Epsilon]\^5\), "+", \(\(283\ \[Epsilon]\^6\)\/40\), "+", \(\(4681\ \[Epsilon]\^7\)\/360\), "+", \(\(123101\ \[Epsilon]\^8\)\/5040\), "-", \(\[Epsilon]\^9\), "+", \(3\ \[Epsilon]\^10\), "-", \(\(20\ \[Epsilon]\^11\)\/3\), "+", \(\(139\ \[Epsilon]\^12\)\/12\), "+", InterpretationBox[\(O[\[Epsilon]]\^13\), SeriesData[ \[Epsilon], 0, {}, 0, 13, 1]]}], SeriesData[ \[Epsilon], 0, {1, 1, 1, Rational[ 3, 2], Rational[ 7, 3], 4, Rational[ 283, 40], Rational[ 4681, 360], Rational[ 123101, 5040], -1, 3, Rational[ -20, 3], Rational[ 139, 12]}, 0, 13, 1]]], "Output"], Cell[BoxData[ InterpretationBox[ RowBox[{ "1", "+", "\[Epsilon]", "+", \(\[Epsilon]\^2\), "+", \(\(3\ \[Epsilon]\^3\)\/2\), "+", \(\(7\ \[Epsilon]\^4\)\/3\), "+", \(4\ \[Epsilon]\^5\), "+", \(\(283\ \[Epsilon]\^6\)\/40\), "+", \(\(4681\ \[Epsilon]\^7\)\/360\), "+", \(\(123101\ \[Epsilon]\^8\)\/5040\), "-", \(\[Epsilon]\^10\), "+", \(\(7\ \[Epsilon]\^11\)\/2\), "-", \(\(17\ \[Epsilon]\^12\)\/2\), "+", InterpretationBox[\(O[\[Epsilon]]\^13\), SeriesData[ \[Epsilon], 0, {}, 0, 13, 1]]}], SeriesData[ \[Epsilon], 0, {1, 1, 1, Rational[ 3, 2], Rational[ 7, 3], 4, Rational[ 283, 40], Rational[ 4681, 360], Rational[ 123101, 5040], 0, -1, Rational[ 7, 2], Rational[ -17, 2]}, 0, 13, 1]]], "Output"], Cell[BoxData[ InterpretationBox[ RowBox[{ "1", "+", "\[Epsilon]", "+", \(\[Epsilon]\^2\), "+", \(\(3\ \[Epsilon]\^3\)\/2\), "+", \(\(7\ \[Epsilon]\^4\)\/3\), "+", \(4\ \[Epsilon]\^5\), "+", \(\(283\ \[Epsilon]\^6\)\/40\), "+", \(\(4681\ \[Epsilon]\^7\)\/360\), "+", \(\(123101\ \[Epsilon]\^8\)\/5040\), "-", \(\[Epsilon]\^11\), "+", \(4\ \[Epsilon]\^12\), "+", InterpretationBox[\(O[\[Epsilon]]\^13\), SeriesData[ \[Epsilon], 0, {}, 0, 13, 1]]}], SeriesData[ \[Epsilon], 0, {1, 1, 1, Rational[ 3, 2], Rational[ 7, 3], 4, Rational[ 283, 40], Rational[ 4681, 360], Rational[ 123101, 5040], 0, 0, -1, 4}, 0, 13, 1]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Series[v, {\[Epsilon], 0, 6}]\)], "Input"], Cell[BoxData[ InterpretationBox[ RowBox[{ "1", "+", "\[Epsilon]", "+", \(\[Epsilon]\^3\), "+", \(\(3\ \[Epsilon]\^4\)\/2\), "+", \(\(17\ \[Epsilon]\^5\)\/6\), "+", \(\(21\ \[Epsilon]\^6\)\/4\), "+", InterpretationBox[\(O[\[Epsilon]]\^7\), SeriesData[ \[Epsilon], 0, {}, 0, 7, 1]]}], SeriesData[ \[Epsilon], 0, {1, 1, 0, 1, Rational[ 3, 2], Rational[ 17, 6], Rational[ 21, 4]}, 0, 7, 1]]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(p = Normal[Series[ Nest[\((\((1 + \[Epsilon])\)\^#)\) &, 1, 12], {\[Epsilon], 0, 12}]]\)], "Input"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3 + 4\ \[Epsilon]\^5 + \(283\ \[Epsilon]\^6\)\/40 + \(4681\ \[Epsilon]\^7\)\ \/360 + \(123101\ \[Epsilon]\^8\)\/5040 + \(118001\ \[Epsilon]\^9\)\/2520 + \ \(98413\ \[Epsilon]\^10\)\/1080 + \(13580899\ \[Epsilon]\^11\)\/75600 + \ \(1020465299\ \[Epsilon]\^12\)\/2851200\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\[IndentingNewLine]dynamic\ \), "\[IndentingNewLine]", \(\ \(f[x_] := \ Power[1 + \[Epsilon], x];\)\), "\[IndentingNewLine]", \(tetra = dynamic\)}], "Input"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \((\(-\ \[Epsilon]\) - \[Epsilon]\^2 - \(3\ \[Epsilon]\^3\)\/2)\)\ \((\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \ Log[1 + \[Epsilon]])\)\^z + \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \((\(-\[Epsilon]\) - \[Epsilon]\^2 \ - \(3\ \[Epsilon]\^3\)\/2)\)\^2\ Log[1 + \[Epsilon]]\^2\ \((\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \ Log[1 + \[Epsilon]])\)\^\(\(-1\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[1 + \ \[Epsilon]])\)\^z)\))\)/\((2\ \((\(-1\) + \((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[ 1 + \[Epsilon]])\))\)\)], "Output"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \((\(-\ \[Epsilon]\) - \[Epsilon]\^2 - \(3\ \[Epsilon]\^3\)\/2)\)\ \((\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \ Log[1 + \[Epsilon]])\)\^z + \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \((\(-\[Epsilon]\) - \[Epsilon]\^2 \ - \(3\ \[Epsilon]\^3\)\/2)\)\^2\ Log[1 + \[Epsilon]]\^2\ \((\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \ Log[1 + \[Epsilon]])\)\^\(\(-1\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[1 + \ \[Epsilon]])\)\^z)\))\)/\((2\ \((\(-1\) + \((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[ 1 + \[Epsilon]])\))\)\)], "Output"], Cell[CellGroupData[{ Cell[BoxData[ \(Series[tetra, {\[Epsilon], 0, 3}, {z, 0, 3}]\)], "Input"], Cell[BoxData[ RowBox[{\(Series[\((\(-\[Epsilon]\) - \[Epsilon]\^2 - \(3\ \ \[Epsilon]\^3\)\/2)\)\ \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\ \^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[1 + \[Epsilon]])\)\^z, {\[Epsilon], 0, 3}]\), "+", \(Series[\((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \((\(-\[Epsilon]\) - \[Epsilon]\^2 \ - \(3\ \[Epsilon]\^3\)\/2)\)\^2\ Log[1 + \[Epsilon]]\^2\ \((\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ \ Log[1 + \[Epsilon]])\)\^\(\(-1\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[1 + \ \[Epsilon]])\)\^z)\))\)/\((2\ \((\(-1\) + \((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)\ Log[ 1 + \[Epsilon]])\))\), {\[Epsilon], 0, 3}]\), "+", RowBox[{"(", InterpretationBox[ RowBox[{ "1", "+", "\[Epsilon]", "+", \(\[Epsilon]\^2\), "+", \(\(3\ \[Epsilon]\^3\)\/2\), "+", InterpretationBox[\(O[\[Epsilon]]\^4\), SeriesData[ \[Epsilon], 0, {}, 0, 4, 1]]}], SeriesData[ \[Epsilon], 0, {1, 1, 1, Rational[ 3, 2]}, 0, 4, 1]], ")"}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[""], "Input"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Normal[ Series[Nest[\((\((1 + \[Epsilon])\)\^#)\) &, 1, 20], {\[Epsilon], 0, 20}]]\)], "Input"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3 + 4\ \[Epsilon]\^5 + \(283\ \[Epsilon]\^6\)\/40 + \(4681\ \[Epsilon]\^7\)\ \/360 + \(123101\ \[Epsilon]\^8\)\/5040 + \(118001\ \[Epsilon]\^9\)\/2520 + \ \(98413\ \[Epsilon]\^10\)\/1080 + \(13580899\ \[Epsilon]\^11\)\/75600 + \ \(1020465299\ \[Epsilon]\^12\)\/2851200 + \(1025863723\ \ \[Epsilon]\^13\)\/1425600 + \(30265674581\ \[Epsilon]\^14\)\/20756736 + \ \(32415942175927\ \[Epsilon]\^15\)\/10897286400 + \(665258961963727\ \ \[Epsilon]\^16\)\/108972864000 + \(6354141051757\ \[Epsilon]\^17\)\/504504000 \ + \(290180321190939427\ \[Epsilon]\^18\)\/11115232128000 + \ \(604021563367509797\ \[Epsilon]\^19\)\/11115232128000 + \ \(1844568291201403213\ \[Epsilon]\^20\)\/16245339264000\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Normal[Series[Log[1 + \[Epsilon]], {\[Epsilon], 0, 6}]]\)], "Input"], Cell[BoxData[ \(\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \[Epsilon]\^4\/4 + \ \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[ExponentialE]\^\(\((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 \ - \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\) z\)\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(z\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \ \[Epsilon]\^3\/3 - \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \ \[Epsilon]\^6\/6)\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(Normal[ Series[\[ExponentialE]\^\(\((\[Epsilon] - \[Epsilon]\^2\/2 + \ \[Epsilon]\^3\/3 - \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\) \ z\), {\[Epsilon], 0, 6}]] // Simplify\), "\[IndentingNewLine]", \(Normal[ Series[\[ExponentialE]\^\(\((\[Epsilon] - \[Epsilon]\^2\/2 + \ \[Epsilon]\^3\/3 - \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\) \ z\), {z, 0, 6}]] // Simplify\)}], "Input"], Cell[BoxData[ \(1\/720\ \((720 + 3\ z\^5\ \((2 - 5\ \[Epsilon])\)\ \[Epsilon]\^5 + z\^6\ \[Epsilon]\^6 + 5\ z\^4\ \[Epsilon]\^4\ \((6 - 12\ \[Epsilon] + 17\ \[Epsilon]\^2)\) - 15\ z\^3\ \[Epsilon]\^3\ \((\(-8\) + 12\ \[Epsilon] - 14\ \[Epsilon]\^2 + 15\ \[Epsilon]\^3)\) + 2\ z\^2\ \[Epsilon]\^2\ \((180 - 180\ \[Epsilon] + 165\ \[Epsilon]\^2 - 150\ \[Epsilon]\^3 + 137\ \[Epsilon]\^4)\) - 12\ z\ \[Epsilon]\ \((\(-60\) + 30\ \[Epsilon] - 20\ \[Epsilon]\^2 + 15\ \[Epsilon]\^3 - 12\ \[Epsilon]\^4 + 10\ \[Epsilon]\^5)\))\)\)], "Output"], Cell[BoxData[ \(1 + z\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\) + 1\/2\ z\^2\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\^2 + 1\/6\ z\^3\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\^3 + 1\/24\ z\^4\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\^4 + 1\/120\ z\^5\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\^5 + 1\/720\ z\^6\ \((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\^6\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Normal[ Series[\[ExponentialE]\^\((\[Epsilon] - \[Epsilon]\^2\/2 + \ \[Epsilon]\^3\/3 - \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\), \ {\[Epsilon], 0, 6}]]\)], "Input"], Cell[BoxData[ \(1 + \[Epsilon]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\[ExponentialE]\^\((\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6)\)\ // ExpandAll\)], "Input"], Cell[BoxData[ \(\[ExponentialE]\^\(\[Epsilon] - \[Epsilon]\^2\/2 + \[Epsilon]\^3\/3 - \ \[Epsilon]\^4\/4 + \[Epsilon]\^5\/5 - \[Epsilon]\^6\/6\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ \(\(dim = 4;\)\), "\[IndentingNewLine]", \(dynamic\), "\[IndentingNewLine]", \(tetra = \(dynamic\ /. \ f\ \[Rule] \ \((Power[1 + \[Epsilon], #] &)\)\) /. \ p \[Rule] Normal[Series[ Nest[\((\((1 + \[Epsilon])\)\^#)\) &, 1, dim], {\[Epsilon], 0, dim}]]\)}], "Input"], Cell[BoxData[ RowBox[{"p", "+", RowBox[{\((1 - p)\), " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], "+", FractionBox[ RowBox[{\(\((1 - p)\)\^2\), " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], \(\(-1\) + z\)], " ", RowBox[{"(", RowBox[{\(-1\), "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], ")"}], " ", RowBox[{ SuperscriptBox["f", "\[Prime]\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], RowBox[{"2", " ", RowBox[{"(", RowBox[{\(-1\), "+", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], ")"}]}]], "+", RowBox[{\(1\/6\), " ", \(\((1 - p)\)\^3\), " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"3", " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], \(\(-2\) + z\)], " ", RowBox[{"(", RowBox[{\(-1\), "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], ")"}], " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]\[Prime]", MultilineFunction->None], "[", "p", "]"}], "2"]}], RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{\(-1\), "+", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], ")"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], \(\(-1\) + z\)], " ", RowBox[{"(", RowBox[{\(-1\), "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}], ")"}], " ", RowBox[{ SuperscriptBox["f", TagBox[\((3)\), Derivative], MultilineFunction->None], "[", "p", "]"}]}], RowBox[{ RowBox[{"(", RowBox[{\(-1\), "+", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}]}], ")"}]}]]}], ")"}]}]}]], "Output"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3 + \((\(-\[Epsilon]\) - \[Epsilon]\^2 - \(3\ \ \[Epsilon]\^3\)\/2 - \(7\ \[Epsilon]\^4\)\/3)\)\ \((\((1 + \[Epsilon])\)\^\(1 \ + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\ \/3\)\ Log[1 + \[Epsilon]])\)\^z + \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] \ + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ \((\(-\ \[Epsilon]\) - \[Epsilon]\^2 - \(3\ \[Epsilon]\^3\)\/2 - \(7\ \[Epsilon]\^4\)\ \/3)\)\^2\ Log[1 + \[Epsilon]]\^2\ \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] \ + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 \ + \[Epsilon]])\)\^\(\(-1\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\)\^z)\))\)/\((2\ \((\(-1\) + \((1 \ + \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \ \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\))\) + 1\/6\ \((\(-\[Epsilon]\) - \[Epsilon]\^2 - \(3\ \[Epsilon]\^3\)\/2 - \ \(7\ \[Epsilon]\^4\)\/3)\)\^3\ \((\((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \ \[Epsilon]]\^3\ \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \ \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\)\^\ \(\(-1\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \ \[Epsilon]])\)\^z)\)\ \((1 + \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \ \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \ \[Epsilon]])\)\^z)\))\)/\((\((\(-1\) + \((1 + \[Epsilon])\)\^\(1 + \[Epsilon] \ + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[ 1 + \[Epsilon]])\)\ \((1 + \((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \ \(7\ \[Epsilon]\^4\)\/3\)\ Log[ 1 + \[Epsilon]])\))\) + \((3\ \((1 + \ \[Epsilon])\)\^\(2\ \((1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3)\)\)\ Log[1 + \[Epsilon]]\^4\ \ \((\((1 + \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \ \[Epsilon]\^3\)\/2 + \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \ \[Epsilon]])\)\^\(\(-2\) + z\)\ \((\(-1\) + \((\((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\)\^z)\)\ \((\(-\((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \ \(7\ \[Epsilon]\^4\)\/3\)\)\ Log[ 1 + \[Epsilon]] + \((\((1 + \[Epsilon])\)\^\(1 + \ \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\)\^z)\))\)/\((\((\(-1\) + \((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \ \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\)\^2\ \((1 + \((1 + \ \[Epsilon])\)\^\(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \ \(7\ \[Epsilon]\^4\)\/3\)\ Log[1 + \[Epsilon]])\))\))\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"p", "+", RowBox[{\((1 - p)\), " ", SuperscriptBox[ RowBox[{ SuperscriptBox["f", "\[Prime]", MultilineFunction->None], "[", "p", "]"}], "z"]}]}]], "Input"], Cell[BoxData[ RowBox[{"p", "+", RowBox[{\((1 - p)\), " ", SuperscriptBox[ RowBox[{ 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Cell[BoxData[ \(Normal[ Series[Nest[\((\((1 + \[Epsilon])\)\^#)\) &, 1, 20], {\[Epsilon], 0, 20}]] /. \ \[Epsilon] \[Rule] \@2. - 1\)], "Input"], Cell[BoxData[ \(1.9811502244984371`\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(Normal[ Series[Nest[\((\((1 + \[Epsilon])\)\^#)\) &, 1, 20], {\[Epsilon], 0, 20}]]\)], "Input"], Cell[BoxData[ \(1 + \[Epsilon] + \[Epsilon]\^2 + \(3\ \[Epsilon]\^3\)\/2 + \(7\ \ \[Epsilon]\^4\)\/3 + 4\ \[Epsilon]\^5 + \(283\ \[Epsilon]\^6\)\/40 + \(4681\ \[Epsilon]\^7\)\ \/360 + \(123101\ \[Epsilon]\^8\)\/5040 + \(118001\ \[Epsilon]\^9\)\/2520 + \ \(98413\ \[Epsilon]\^10\)\/1080 + \(13580899\ \[Epsilon]\^11\)\/75600 + \ \(1020465299\ \[Epsilon]\^12\)\/2851200 + \(1025863723\ \ \[Epsilon]\^13\)\/1425600 + \(30265674581\ \[Epsilon]\^14\)\/20756736 + \ \(32415942175927\ \[Epsilon]\^15\)\/10897286400 + \(665258961963727\ \ \[Epsilon]\^16\)\/108972864000 + \(6354141051757\ \[Epsilon]\^17\)\/504504000 \ + \(290180321190939427\ 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3.71127 m .36697 3.71127 L s [(0.008)] .34822 3.71127 1 0 Mshowa .36072 4.61094 m .36697 4.61094 L s [(0.01)] .34822 4.61094 1 0 Mshowa .125 Mabswid .36072 .33753 m .36447 .33753 L s .36072 .56244 m .36447 .56244 L s .36072 .78736 m .36447 .78736 L s .36072 1.23719 m .36447 1.23719 L s .36072 1.46211 m .36447 1.46211 L s .36072 1.68702 m .36447 1.68702 L s .36072 2.13686 m .36447 2.13686 L s .36072 2.36177 m .36447 2.36177 L s .36072 2.58669 m .36447 2.58669 L s .36072 3.03652 m .36447 3.03652 L s .36072 3.26144 m .36447 3.26144 L s .36072 3.48636 m .36447 3.48636 L s .36072 3.93619 m .36447 3.93619 L s .36072 4.16111 m .36447 4.16111 L s .36072 4.38602 m .36447 4.38602 L s .25 Mabswid .36072 0 m .36072 4.72995 L s .5 Mabswid .36073 .11262 m .62751 1.03109 L .77575 1.73263 L .82825 2.07766 L .85979 2.35895 L .87162 2.50232 L .87642 2.57452 L .88052 2.64865 L .88556 2.77842 L .88764 2.89135 L .88747 3.00151 L .88548 3.09673 L .88124 3.20033 L .87551 3.29288 L .86896 3.37316 L .86192 3.44375 L .84309 3.59063 L .81865 3.73385 L .79426 3.84791 L .73564 4.05707 L .67557 4.21545 L .623 4.32454 L .57132 4.41185 L .52151 4.48053 L .45442 4.55195 L .42617 4.57503 L .40402 4.59012 L .3865 4.60004 L .37094 4.6072 L .36038 4.61105 L .35083 4.61373 L .34634 4.61468 L .3426 4.61531 L .3391 4.61574 L .33732 4.61589 L .33657 4.61594 L .33579 4.61599 L .33454 4.61604 L .33344 4.61606 L .3328 4.61607 L .33221 4.61607 L .33115 4.61605 L .3301 4.616 L .32919 4.61595 L .32826 4.61587 L .32733 4.61578 L .32578 4.61557 L .32449 4.61534 L .32245 4.61486 L .32074 4.61431 L Mistroke .31933 4.61372 L .31764 4.61278 L .31673 4.61207 L .3164 4.61173 L .31614 4.61143 L .31599 4.61121 L .31587 4.61101 L .3158 4.61087 L .31575 4.61074 L .31572 4.61064 L .31571 4.61057 L .3157 4.61053 L .3157 4.6105 L .31569 4.61048 L .31569 4.61047 L .31569 4.61046 L .31569 4.61045 L .31569 4.61045 L .31569 4.61044 L .31569 4.61043 L .31569 4.61042 L .31569 4.61041 L .31569 4.6104 L .31569 4.61039 L .3157 4.61038 L .3157 4.61037 L .3157 4.61035 L .3157 4.61034 L .31571 4.61032 L .31571 4.61031 L .31572 4.6103 L .31573 4.61028 L .31574 4.61027 L .31574 4.61027 L .31574 4.61027 L .31574 4.61027 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L Mistroke .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L Mistroke .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L Mistroke .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L Mistroke .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L .31575 4.61026 L Mfstroke .36073 .11262 m .61987 .85322 L .80144 1.52922 L .86145 1.81792 L .90438 2.06914 L .93285 2.27629 L .95498 2.48738 L .96975 2.70035 L .97619 2.90555 L .97514 3.07816 L .96912 3.22578 L .95696 3.38331 L .94197 3.51344 L .92115 3.64845 L .89875 3.76305 L .85324 3.94311 L .80193 4.09739 L .71112 4.29857 L .65994 4.3848 L .61607 4.44678 L .54639 4.52561 L .49036 4.57279 L .46612 4.58867 L .44702 4.59912 L .4204 4.6103 L .40941 4.61359 L .39961 4.61575 L .39493 4.61649 L .39104 4.61694 L .38917 4.6171 L .38721 4.61722 L .3853 4.6173 L .38361 4.61733 L .38219 4.61732 L .38078 4.61729 L .37845 4.61716 L .37726 4.61706 L .3762 4.61695 L .37403 4.61666 L .37229 4.61635 L .37083 4.61603 L .36849 4.61539 L .36648 4.61467 L .36478 4.61392 L .36272 4.61271 L .36151 4.61176 L .36072 4.61094 L .36026 4.61027 L .36012 4.61002 L .36002 4.60978 L Mistroke .35996 4.6096 L .35994 4.60953 L .35992 4.60947 L .35991 4.60941 L .3599 4.60935 L .3599 4.60931 L .3599 4.60927 L .35989 4.60923 L .35989 4.60919 L .35989 4.60917 L .35989 4.60916 L .3599 4.60913 L .3599 4.6091 L .3599 4.60907 L .35991 4.60905 L .35991 4.60903 L .35993 4.60898 L .35994 4.60895 L .35995 4.60894 L .35996 4.60891 L .35998 4.6089 L .35998 4.6089 L .35999 4.60889 L .35999 4.60889 L .35999 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L Mistroke .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L Mistroke .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L Mistroke .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L .36001 4.60889 L Mfstroke .36072 .11263 m .19666 1.0704 L .13521 1.51021 L .0922 1.87752 L .06325 2.18191 L .04197 2.47565 L .03026 2.713 L .0248 2.90965 L .02381 3.11752 L .02724 3.29017 L .03481 3.45772 L .04635 3.61536 L .06111 3.75813 L .07687 3.87567 L .10885 4.05612 L .14097 4.19221 L .17379 4.30225 L .22559 4.43504 L .27271 4.52317 L .30288 4.56562 L .32411 4.58889 L .33867 4.60126 L .3484 4.60747 L .35128 4.60889 L .35367 4.60988 L .3554 4.61046 L .35662 4.61079 L .35759 4.61099 L .35795 4.61105 L .35831 4.6111 L .35865 4.61113 L .35881 4.61115 L .35896 4.61116 L .35919 4.61116 L .35941 4.61117 L .35952 4.61116 L .35963 4.61116 L .35973 4.61116 L .35982 4.61115 L .35996 4.61114 L .36009 4.61112 L .36029 4.61108 L .36045 4.61105 L .36063 4.61098 L .3607 4.61095 L .36074 4.61093 L .3608 4.61089 L .36083 4.61086 L .36084 4.61085 L .36085 4.61084 L Mistroke .36085 4.61084 L .36085 4.61083 L .36085 4.61083 L .36085 4.61083 L .36085 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61083 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36086 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L Mistroke .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L Mistroke .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L .36085 4.61082 L Mfstroke .36072 .11263 m .36005 .75777 L .35654 1.26331 L .351 1.76434 L .34547 2.16838 L .3368 2.75611 L .33068 3.22502 L .3288 3.42103 L .32766 3.60496 L .32736 3.74739 L .32761 3.86246 L .32842 3.97833 L .32954 4.06856 L .33028 4.11273 L .33116 4.15684 L .33293 4.22741 L .33679 4.33828 L .34032 4.41086 L .34411 4.47101 L .34727 4.51105 L .35173 4.55594 L .35514 4.5824 L .3574 4.5964 L .35884 4.60382 L .36008 4.60897 L .36055 4.61052 L .36068 4.61085 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L Mistroke .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L .36073 4.61095 L Mfstroke .36073 .11264 m .443 .84852 L .48962 1.41491 L .52008 1.96498 L .53299 2.39852 L .53569 2.73645 L .53285 3.0027 L .52584 3.25184 L .51566 3.47411 L .50391 3.66077 L .49058 3.8276 L .4669 4.05857 L .42302 4.362 L .3945 4.50166 L .37895 4.5611 L .36613 4.59961 L .36219 4.6085 L .36108 4.61047 L .36079 4.61086 L .36074 4.61093 L .36073 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mistroke .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mfstroke .36073 .11264 m .51659 .93039 L .60251 1.55171 L .65576 2.14519 L .67534 2.6036 L .67594 2.95349 L .66672 3.22348 L .64978 3.47059 L .62737 3.68562 L .60276 3.86143 L .57587 4.01408 L .53002 4.2166 L .48401 4.37119 L .45097 4.45959 L .40741 4.55079 L .38243 4.58954 L .37097 4.60308 L .36567 4.60799 L .36276 4.61008 L .36162 4.61069 L .3613 4.61082 L .36109 4.61089 L .36101 4.61091 L .36094 4.61092 L .36089 4.61093 L .36086 4.61094 L .36083 4.61094 L .36082 4.61094 L .36081 4.61094 L .36079 4.61095 L .36078 4.61095 L .36077 4.61095 L .36077 4.61095 L .36076 4.61095 L .36075 4.61095 L .36075 4.61094 L .36075 4.61094 L .36074 4.61094 L .36074 4.61094 L .36073 4.61094 L .36073 4.61094 L .36073 4.61094 L .36073 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mistroke .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mistroke .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mfstroke .36072 .11264 m .26767 1.68149 L .23624 2.29875 L .2185 2.76336 L .21063 3.11268 L .20944 3.4185 L .21326 3.64272 L .2197 3.81269 L .22969 3.97642 L .24039 4.0997 L .25274 4.20802 L .26597 4.29948 L .2907 4.42746 L .30931 4.49848 L .33485 4.5696 L .34368 4.58773 L .34932 4.59746 L .35538 4.60603 L .35845 4.60936 L .35986 4.61051 L .36039 4.61083 L .36051 4.61088 L .36059 4.61091 L .36064 4.61093 L .36067 4.61094 L .36068 4.61094 L .36069 4.61094 L .3607 4.61094 L .3607 4.61094 L .3607 4.61094 L .3607 4.61094 L .36071 4.61094 L .36071 4.61094 L .36071 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L Mistroke .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L .36072 4.61094 L 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