(************** 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[ 43144, 750]*) (*NotebookOutlinePosition[ 44116, 779]*) (* CellTagsIndexPosition[ 44072, 775]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell[BoxData[ \(chi[t_, y_] = \((Q + f1[y]*t + \((f2[y]/2)\)*t^2)\) + Log[t]*P*\((1 - \((1/4)\)*k^2*t^2)\)\)], "Input"], Cell[BoxData[ \(Q + t\ f1[y] + 1\/2\ t\^2\ f2[y] + P\ \((1 - \(k\^2\ t\^2\)\/4)\)\ Log[t]\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\ \(eq1 = t* Normal[Series[\((1/t)\)*\((\(-D[t*D[chi[t, y], t], t]\) - 3*D[p[t, y], t]*t* D[chi[t, y], t] + \((1/t^2)\) \((D[t*D[chi[t, y], y], y] + 3*D[p[t, y], y]*t*D[chi[t, y], y])\))\) - \((k^2/ q[t, y]^2)\)*chi[t, y], {t, 0, \(-1\)}]]\)\)\)], "Input"], Cell[BoxData[ RowBox[{\(-\(\(P\ \((\((\(-6\) + L\^2\ rm)\)\ Cosh[ 1\/2\ \((v0 - 2\ y)\)] + \((6 + L\^2\ rp)\)\ Cosh[ v0\/2 + y])\)\ Csch[v0]\)\/\(2\ L\)\)\), "-", \(f1[y]\), "+", RowBox[{ SuperscriptBox["f1", "\[Prime]\[Prime]", MultilineFunction->None], "[", "y", "]"}]}]], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\ \(s1 = c1*Sinh[vp] + c2*Cosh[vp]\[IndentingNewLine] s2 = c1*Sinh[vm] + c2*Cosh[vm]\[IndentingNewLine]\[IndentingNewLine] ff1[y_] = Simplify[f1[ y] /. \(DSolve[{eq1 \[Equal] 0, \(f1'\)[vp] \[Equal] s1, \(f1'\)[vm] \[Equal] s2}, f1, y]\)[\([1]\)]]\)\)\)], "Input"], Cell[BoxData[ \(c2\ Cosh[v0\/2] + c1\ Sinh[v0\/2]\)], "Output"], Cell[BoxData[ \(c2\ Cosh[v0\/2] - c1\ Sinh[v0\/2]\)], "Output"], Cell[BoxData[ \(\(\(1\/\(8\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ L\)\)\((\ \[ExponentialE]\^\(-y\)\ \((4\ c2\ \((\(-1\) + \[ExponentialE]\^\(2\ \ v0\))\)\^2\ \((\(-1\) + \[ExponentialE]\^\(2\ y\))\)\ L + 4\ c1\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \((1 + \ \[ExponentialE]\^\(2\ y\))\)\ L - \[ExponentialE]\^\(v0/2\)\ P\ \((\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((2 + v0 - 2\ y)\) + \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ \ \((\(-6\) + L\^2\ rm)\)\ \((2 + 3\ v0 - 2\ y)\) + \[ExponentialE]\^\(2\ y\)\ \((\(-6\) + L\^2\ rm)\)\ \((\(-2\) + v0 + 2\ y)\) + \[ExponentialE]\^\(3\ v0\)\ \((\(-6\) + L\^2\ rm)\)\ \((2 + v0 + 2\ y)\) + \[ExponentialE]\^\(v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((\(-2\) + 3\ v0 + 2\ y)\) + \[ExponentialE]\^\(2\ v0\)\ \((6 + L\^2\ rp)\)\ \((2 + 3\ v0 + 2\ y)\) + \((6 + L\^2\ rp)\)\ \((v0 - 2\ \((1 + y)\))\) + \[ExponentialE]\^v0\ \((\(-6\) + L\^2\ rm)\)\ \((3\ v0 - 2\ \((1 + y)\))\))\))\))\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\(chi1[t_, y_] = \((Q + ff1[y]*t + \((f2[y]/2)\)*t^2)\) + Log[t]*P \((1 - \((1/4)\)*k^2* t^2)\);\)\[IndentingNewLine]\[IndentingNewLine] eq2 = SeriesCoefficient[ Series[\((1/t)\)*\((\(-D[t*D[chi1[t, y], t], t]\) - 3*D[p[t, y], t]*t* D[chi1[t, y], t] + \((1/t^2)\) \((D[t*D[chi1[t, y], y], y] + 3*D[p[t, y], y]*t*D[chi1[t, y], y])\))\) - \((k^2/ q[t, y]^2)\)*chi1[t, y], {t, 0, 0}], 0]\)\)\)], "Input"], Cell[BoxData[ RowBox[{\(k\^2\ P\), "-", \(3\ \((\(\(1\/\(48\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \ L\^2\)\)\((\[ExponentialE]\^\(-y\)\ \((4\ c2\ \((\(-1\) + \ \[ExponentialE]\^\(2\ v0\))\)\^2\ \((\(-1\) + \[ExponentialE]\^\(2\ y\))\)\ L \ + 4\ c1\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \((1 + \[ExponentialE]\ \^\(2\ y\))\)\ L - \[ExponentialE]\^\(v0/2\)\ P\ \((\[ExponentialE]\^\(3\ v0 \ + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((2 + v0 - 2\ y)\) + \[ExponentialE]\^\(2\ \((v0 + \ y)\)\)\ \((\(-6\) + L\^2\ rm)\)\ \((2 + 3\ v0 - 2\ y)\) + \[ExponentialE]\^\(2\ y\)\ \ \((\(-6\) + L\^2\ rm)\)\ \((\(-2\) + v0 + 2\ y)\) + \[ExponentialE]\^\(3\ v0\)\ \((\(-6\ \) + L\^2\ rm)\)\ \((2 + v0 + 2\ y)\) + \[ExponentialE]\^\(v0 + 2\ y\)\ \ \((6 + L\^2\ rp)\)\ \((\(-2\) + 3\ v0 + 2\ y)\) + \[ExponentialE]\^\(2\ v0\)\ \((6 + L\^2\ rp)\)\ \((2 + 3\ v0 + 2\ y)\) + \((6 + L\^2\ rp)\)\ \((v0 - 2\ \((1 + y)\))\) + \[ExponentialE]\^v0\ \ \((\(-6\) + L\^2\ rm)\)\ \((3\ v0 - 2\ \((1 + y)\))\))\))\)\ \((\((\(-6\) + L\^2\ rm)\)\ Cosh[ 1\/2\ \((v0 - 2\ y)\)] + \((6 + L\^2\ rp)\)\ Cosh[ v0\/2 + y])\)\ Csch[ v0])\)\) - \(\(1\/\(72\ L\^2\)\)\((P\ \((144 - 36\ L\^2\ rm + 3\ L\^4\ rm\^2 + 36\ L\^2\ rp + 3\ L\^4\ rp\^2 + 6\ \((\(-6\) + L\^2\ rm)\)\ \((6 + L\^2\ rp)\)\ Cosh[ v0] + 72\ Cosh[2\ v0] - 36\ Cosh[v0 - 2\ y] - 36\ L\^2\ rm\ Cosh[v0 - 2\ y] + 7\ L\^4\ rm\^2\ Cosh[v0 - 2\ y] + 72\ Cosh[2\ y] + 36\ L\^2\ rm\ Cosh[2\ y] - 36\ L\^2\ rp\ Cosh[2\ y] + 14\ L\^4\ rm\ rp\ Cosh[2\ y] - 36\ Cosh[v0 + 2\ y] + 36\ L\^2\ rp\ Cosh[v0 + 2\ y] + 7\ L\^4\ rp\^2\ Cosh[v0 + 2\ y])\)\ Csch[v0]\^2)\)\))\)\), "-", \(2\ f2[y]\), "+", \(k\^2\ P\ Log[t]\), "+", \(k\^2\ \((\(-Q\) - P\ Log[t])\)\), "+", \(\(1\/\(2\ L\)\)\((\((\(\(1\/\(8\ \((\(-1\) + \ \[ExponentialE]\^\(2\ v0\))\)\^2\ L\)\)\((\[ExponentialE]\^\(-y\)\ \((8\ c1\ \ \[ExponentialE]\^\(2\ y\)\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ L + 8\ c2\ \[ExponentialE]\^\(2\ y\)\ \((\(-1\) + \ \[ExponentialE]\^\(2\ v0\))\)\^2\ L - \[ExponentialE]\^\(v0/2\)\ P\ \((\(-2\)\ \ \[ExponentialE]\^v0\ \((\(-6\) + L\^2\ rm)\) + 2\ \[ExponentialE]\^\(3\ v0\)\ \((\(-6\) + L\^2\ rm)\) + 2\ \[ExponentialE]\^\(2\ y\)\ \((\(-6\) + L\^2\ rm)\) - 2\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ \ \((\(-6\) + L\^2\ rm)\) - 2\ \((6 + L\^2\ rp)\) + 2\ \[ExponentialE]\^\(2\ v0\)\ \((6 + L\^2\ rp)\) + 2\ \[ExponentialE]\^\(v0 + 2\ y\)\ \((6 + L\^2\ rp)\) - 2\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ \((6 + L\^2\ rp)\) + 2\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((2 + v0 - 2\ y)\) + 2\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ \ \((\(-6\) + L\^2\ rm)\)\ \((2 + 3\ v0 - 2\ y)\) + 2\ \[ExponentialE]\^\(2\ y\)\ \((\(-6\) + L\^2\ rm)\)\ \((\(-2\) + v0 + 2\ y)\) + 2\ \[ExponentialE]\^\(v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((\(-2\) + 3\ v0 + 2\ y)\))\))\))\)\) - \(\(1\/\(8\ \((\(-1\) \ + \[ExponentialE]\^\(2\ v0\))\)\^2\ L\)\)\((\[ExponentialE]\^\(-y\)\ \((4\ c2\ \ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \((\(-1\) + \[ExponentialE]\^\ \(2\ y\))\)\ L + 4\ c1\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \ \((1 + \[ExponentialE]\^\(2\ y\))\)\ L - \[ExponentialE]\^\(v0/2\)\ P\ \((\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((2 + v0 - 2\ y)\) + \[ExponentialE]\^\(2\ \((v0 + \ y)\)\)\ \((\(-6\) + L\^2\ rm)\)\ \((2 + 3\ v0 - 2\ y)\) + \[ExponentialE]\^\(2\ y\)\ \ \((\(-6\) + L\^2\ rm)\)\ \((\(-2\) + v0 + 2\ y)\) + \[ExponentialE]\^\(3\ v0\)\ \ \((\(-6\) + L\^2\ rm)\)\ \((2 + v0 + 2\ y)\) + \[ExponentialE]\^\(v0 + 2\ y\)\ \ \((6 + L\^2\ rp)\)\ \((\(-2\) + 3\ v0 + 2\ y)\) + \[ExponentialE]\^\(2\ v0\)\ \((6 \ + L\^2\ rp)\)\ \((2 + 3\ v0 + 2\ y)\) + \((6 + L\^2\ rp)\)\ \((v0 - 2\ \((1 + y)\))\) + \[ExponentialE]\^v0\ \ \((\(-6\) + L\^2\ rm)\)\ \((3\ v0 - 2\ \((1 + y)\))\))\))\))\)\))\)\ Csch[ v0]\ \((\(-\((\(-6\) + L\^2\ rm)\)\)\ Sinh[ 1\/2\ \((v0 - 2\ y)\)] + \((6 + L\^2\ rp)\)\ Sinh[ v0\/2 + y])\))\)\), "+", FractionBox[ RowBox[{ SuperscriptBox["f2", "\[Prime]\[Prime]", MultilineFunction->None], "[", "y", "]"}], "2"]}]], "Output"] }, Open ]], Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\)\)], "Input"], Cell[BoxData[""], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\ \(ff2[y_] = Simplify[Normal[ f2[y] /. \(DSolve[{eq2 \[Equal] 0, \(f2'\)[vp] \[Equal] b1, \(f2'\)[vm] \[Equal] b2}, f2, y]\)[\([1]\)]]]\)\)\)], "Input"], Cell[BoxData[ \(\(\(1\/\(96\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^3\ \((1 + \ \[ExponentialE]\^\(2\ v0\))\)\ L\^2\)\)\((\[ExponentialE]\^\(\(-2\)\ y\)\ \((\ \(-48\)\ b2\ \[ExponentialE]\^\(3\ v0\)\ L\^2 + 96\ b2\ \[ExponentialE]\^\(5\ v0\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(7\ v0\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2 + 96\ b2\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2 + 48\ b1\ \[ExponentialE]\^v0\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\ \))\)\^2\ \((1 + \[ExponentialE]\^\(2\ v0 + 4\ y\))\)\ L\^2 - 36\ \[ExponentialE]\^v0\ P + 72\ \[ExponentialE]\^\(2\ v0\)\ P - 36\ \[ExponentialE]\^\(3\ v0\)\ P + 36\ \[ExponentialE]\^\(5\ v0\)\ P - 72\ \[ExponentialE]\^\(6\ v0\)\ P + 36\ \[ExponentialE]\^\(7\ v0\)\ P - 288\ \[ExponentialE]\^\(2\ y\)\ P - 2016\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ P + 1296\ \[ExponentialE]\^\(v0 + 2\ y\)\ P + 1296\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ P - 1296\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ P + 2016\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ P - 1296\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ P + 288\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ P - 36\ \[ExponentialE]\^\(v0 + 4\ y\)\ P + 72\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P - 36\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P + 36\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P - 72\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P + 36\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P - 48\ \[ExponentialE]\^\(2\ y\)\ k\^2\ L\^2\ P + 96\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ k\^2\ L\^2\ P - 96\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ k\^2\ L\^2\ P + 48\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ k\^2\ L\^2\ P + 48\ \[ExponentialE]\^\(2\ y\)\ k\^2\ L\^2\ Q - 96\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ k\^2\ L\^2\ Q + 96\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ k\^2\ L\^2\ Q - 48\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ k\^2\ L\^2\ Q - 24\ c1\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(3\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(5\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(7\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(9\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(11\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(13\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(15\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm + 432\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rm - 216\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rm - 216\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rm + 216\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rm - 432\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rm + 216\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm - 17\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2 + 17\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2 - 36\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rm\^2 + 36\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rm\^2 - 17\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2 + 17\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2 - 24\ c2\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ \((\(-1\) + \ \[ExponentialE]\^v0)\)\^3\ \((1 + \[ExponentialE]\^v0)\)\^2\ \((1 + \ \[ExponentialE]\^\(2\ v0\))\)\ L\ \((\(-12\) + L\^2\ \((rm - rp)\))\) - 24\ c1\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(3\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(5\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(7\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(9\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(11\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(13\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(15\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 108\ \[ExponentialE]\^v0\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp - 432\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rp + 216\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rp + 216\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rp - 216\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rp + 432\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rp - 216\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp - 34\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp + 34\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp - 36\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^4\ P\ rm\ rp - 36\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp + 36\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp + 36\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp - 34\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp + 34\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp - 17\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2 + 17\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2 - 36\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rp\^2 + 36\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rp\^2 - 17\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2 + 17\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2 + 36\ \[ExponentialE]\^v0\ P\ v0 - 72\ \[ExponentialE]\^\(2\ v0\)\ P\ v0 + 108\ \[ExponentialE]\^\(3\ v0\)\ P\ v0 - 144\ \[ExponentialE]\^\(4\ v0\)\ P\ v0 + 108\ \[ExponentialE]\^\(5\ v0\)\ P\ v0 - 72\ \[ExponentialE]\^\(6\ v0\)\ P\ v0 + 36\ \[ExponentialE]\^\(7\ v0\)\ P\ v0 + 1728\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ P\ v0 - 144\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ P\ v0 - 432\ \[ExponentialE]\^\(v0 + 2\ y\)\ P\ v0 - 3024\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ P\ v0 + 3456\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ P\ v0 - 3024\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ P\ v0 + 1728\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ P\ v0 - 432\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ P\ v0 + 36\ \[ExponentialE]\^\(v0 + 4\ y\)\ P\ v0 - 72\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P\ v0 - 72\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P\ v0 + 36\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm\ v0 - 324\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm\ v0 + 216\ \[ExponentialE]\^\(4\ v0\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm\ v0 - 108\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm\ v0 - 288\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rm\ v0 + 216\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^2\ P\ rm\ v0 + 72\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 504\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 576\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 504\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 288\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 72\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 108\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 - 324\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 51\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2\ v0 + 17\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2\ v0 + 24\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rm\^2\ v0 + 48\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^4\ P\ rm\^2\ v0 + 24\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rm\^2\ v0 + 17\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2\ v0 + 51\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2\ v0 + 108\ \[ExponentialE]\^v0\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp\ v0 - 216\ \[ExponentialE]\^\(4\ v0\)\ L\^2\ P\ rp\ v0 + 324\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp\ v0 + 288\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rp\ v0 - 216\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^2\ P\ rp\ v0 - 72\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 504\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 + 576\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 504\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 + 288\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 72\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 324\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 108\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 34\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 68\ \[ExponentialE]\^\(4\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 68\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^4\ P\ rm\ rp\ v0 + 12\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 84\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 84\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 12\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ v0 + 17\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2\ v0 + 51\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2\ v0 + 24\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rp\^2\ v0 + 48\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^4\ P\ rp\^2\ v0 + 24\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rp\^2\ v0 + 51\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ v0 + 17\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ v0 - 72\ \[ExponentialE]\^v0\ P\ y + 144\ \[ExponentialE]\^\(2\ v0\)\ P\ y - 72\ \[ExponentialE]\^\(3\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(5\ v0\)\ P\ y - 144\ \[ExponentialE]\^\(6\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(7\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(v0 + 4\ y\)\ P\ y - 144\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P\ y + 72\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P\ y - 72\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P\ y + 144\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P\ y - 72\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P\ y - 216\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm\ y - 34\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2\ y + 34\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2\ y + 34\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2\ y - 34\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2\ y - 216\ \[ExponentialE]\^v0\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp\ y - 68\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp\ y + 68\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp\ y + 68\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ y - 68\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ y - 34\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2\ y + 34\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2\ y + 34\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ y - 34\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ \ y)\))\)\)\)], "Output"] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ \(\(\(\[IndentingNewLine]\)\(chi2[t_, y_] = \((Q + ff1[y]*t + \((ff2[y]/2)\)*t^2)\) + Log[t]*P \((1 - \((1/4)\)*k^2*t^2)\)\)\)\)], "Input"], Cell[BoxData[ \(Q + \(\(1\/\(192\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^3\ \((1 + \ \[ExponentialE]\^\(2\ v0\))\)\ L\^2\)\)\((\[ExponentialE]\^\(\(-2\)\ y\)\ \ t\^2\ \((\(-48\)\ b2\ \[ExponentialE]\^\(3\ v0\)\ L\^2 + 96\ b2\ \[ExponentialE]\^\(5\ v0\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(7\ v0\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2 + 96\ b2\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2 - 48\ b2\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2 + 48\ b1\ \[ExponentialE]\^v0\ \((\(-1\) + \[ExponentialE]\^\(2\ \ v0\))\)\^2\ \((1 + \[ExponentialE]\^\(2\ v0 + 4\ y\))\)\ L\^2 - 36\ \[ExponentialE]\^v0\ P + 72\ \[ExponentialE]\^\(2\ v0\)\ P - 36\ \[ExponentialE]\^\(3\ v0\)\ P + 36\ \[ExponentialE]\^\(5\ v0\)\ P - 72\ \[ExponentialE]\^\(6\ v0\)\ P + 36\ \[ExponentialE]\^\(7\ v0\)\ P - 288\ \[ExponentialE]\^\(2\ y\)\ P - 2016\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ P + 1296\ \[ExponentialE]\^\(v0 + 2\ y\)\ P + 1296\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ P - 1296\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ P + 2016\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ P - 1296\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ P + 288\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ P - 36\ \[ExponentialE]\^\(v0 + 4\ y\)\ P + 72\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P - 36\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P + 36\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P - 72\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P + 36\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P - 48\ \[ExponentialE]\^\(2\ y\)\ k\^2\ L\^2\ P + 96\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ k\^2\ L\^2\ P - 96\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ k\^2\ L\^2\ P + 48\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ k\^2\ L\^2\ P + 48\ \[ExponentialE]\^\(2\ y\)\ k\^2\ L\^2\ Q - 96\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ k\^2\ L\^2\ Q + 96\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ k\^2\ L\^2\ Q - 48\ \[ExponentialE]\^\(8\ v0 + 2\ y\)\ k\^2\ L\^2\ Q - 24\ c1\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(3\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(5\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(7\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(9\ v0\)\/2 + 2\ y\)\ L\^3\ rm + 24\ c1\ \[ExponentialE]\^\(\(11\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(13\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 24\ c1\ \[ExponentialE]\^\(\(15\ v0\)\/2 + 2\ y\)\ L\^3\ rm - 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm + 432\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rm - 216\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rm - 216\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rm + 216\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rm - 432\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rm + 216\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm - 108\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm + 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm - 17\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2 + 17\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2 - 36\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rm\^2 + 36\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rm\^2 - 17\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2 + 17\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2 - 24\ c2\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ \((\(-1\) + \ \[ExponentialE]\^v0)\)\^3\ \((1 + \[ExponentialE]\^v0)\)\^2\ \((1 + \ \[ExponentialE]\^\(2\ v0\))\)\ L\ \((\(-12\) + L\^2\ \((rm - rp)\))\) - 24\ c1\ \[ExponentialE]\^\(v0\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(3\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(5\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(7\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(9\ v0\)\/2 + 2\ y\)\ L\^3\ rp + 24\ c1\ \[ExponentialE]\^\(\(11\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(13\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 24\ c1\ \[ExponentialE]\^\(\(15\ v0\)\/2 + 2\ y\)\ L\^3\ rp - 108\ \[ExponentialE]\^v0\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp - 432\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rp + 216\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rp + 216\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rp - 216\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rp + 432\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rp - 216\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp - 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp + 108\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp - 34\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp + 34\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp - 36\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^4\ P\ rm\ rp - 36\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp + 36\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp + 36\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp - 34\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp + 34\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp - 17\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2 + 17\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2 - 36\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rp\^2 + 36\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rp\^2 - 17\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2 + 17\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2 + 36\ \[ExponentialE]\^v0\ P\ v0 - 72\ \[ExponentialE]\^\(2\ v0\)\ P\ v0 + 108\ \[ExponentialE]\^\(3\ v0\)\ P\ v0 - 144\ \[ExponentialE]\^\(4\ v0\)\ P\ v0 + 108\ \[ExponentialE]\^\(5\ v0\)\ P\ v0 - 72\ \[ExponentialE]\^\(6\ v0\)\ P\ v0 + 36\ \[ExponentialE]\^\(7\ v0\)\ P\ v0 + 1728\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ P\ v0 - 144\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ P\ v0 - 432\ \[ExponentialE]\^\(v0 + 2\ y\)\ P\ v0 - 3024\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ P\ v0 + 3456\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ P\ v0 - 3024\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ P\ v0 + 1728\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ P\ v0 - 432\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ P\ v0 + 36\ \[ExponentialE]\^\(v0 + 4\ y\)\ P\ v0 - 72\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P\ v0 - 72\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P\ v0 + 36\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P\ v0 + 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm\ v0 - 324\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm\ v0 + 216\ \[ExponentialE]\^\(4\ v0\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm\ v0 - 108\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm\ v0 - 288\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rm\ v0 + 216\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^2\ P\ rm\ v0 + 72\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 504\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 576\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 504\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 288\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 + 72\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rm\ v0 - 108\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 - 324\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm\ v0 + 51\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2\ v0 + 17\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2\ v0 + 24\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rm\^2\ v0 + 48\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^4\ P\ rm\^2\ v0 + 24\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rm\^2\ v0 + 17\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2\ v0 + 51\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2\ v0 + 108\ \[ExponentialE]\^v0\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp\ v0 - 216\ \[ExponentialE]\^\(4\ v0\)\ L\^2\ P\ rp\ v0 + 324\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp\ v0 + 288\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^2\ P\ rp\ v0 - 216\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^2\ P\ rp\ v0 - 72\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 504\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 + 576\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 504\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 + 288\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 72\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 324\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 - 108\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 108\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp\ v0 + 34\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 68\ \[ExponentialE]\^\(4\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp\ v0 + 68\ \[ExponentialE]\^\(4\ \((v0 + y)\)\)\ L\^4\ P\ rm\ rp\ v0 + 12\ \[ExponentialE]\^\(v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 84\ \[ExponentialE]\^\(3\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 84\ \[ExponentialE]\^\(5\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 12\ \[ExponentialE]\^\(7\ v0 + 2\ y\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ v0 + 34\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ v0 + 17\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2\ v0 + 51\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2\ v0 + 24\ \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ L\^4\ P\ rp\^2\ v0 + 48\ \[ExponentialE]\^\(4\ v0 + 2\ y\)\ L\^4\ P\ rp\^2\ v0 + 24\ \[ExponentialE]\^\(6\ v0 + 2\ y\)\ L\^4\ P\ rp\^2\ v0 + 51\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ v0 + 17\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ v0 - 72\ \[ExponentialE]\^v0\ P\ y + 144\ \[ExponentialE]\^\(2\ v0\)\ P\ y - 72\ \[ExponentialE]\^\(3\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(5\ v0\)\ P\ y - 144\ \[ExponentialE]\^\(6\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(7\ v0\)\ P\ y + 72\ \[ExponentialE]\^\(v0 + 4\ y\)\ P\ y - 144\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ P\ y + 72\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ P\ y - 72\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ P\ y + 144\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ P\ y - 72\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ P\ y - 216\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(3\ v0\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(7\ v0\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rm\ y + 216\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^2\ P\ rm\ y - 216\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rm\ y - 34\ \[ExponentialE]\^\(3\ v0\)\ L\^4\ P\ rm\^2\ y + 34\ \[ExponentialE]\^\(7\ v0\)\ L\^4\ P\ rm\^2\ y + 34\ \[ExponentialE]\^\(v0 + 4\ y\)\ L\^4\ P\ rm\^2\ y - 34\ \[ExponentialE]\^\(5\ v0 + 4\ y\)\ L\^4\ P\ rm\^2\ y - 216\ \[ExponentialE]\^v0\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(2\ v0\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(5\ v0\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(6\ v0\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^2\ P\ rp\ y + 216\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^2\ P\ rp\ y - 216\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^2\ P\ rp\ y - 68\ \[ExponentialE]\^\(2\ v0\)\ L\^4\ P\ rm\ rp\ y + 68\ \[ExponentialE]\^\(6\ v0\)\ L\^4\ P\ rm\ rp\ y + 68\ \[ExponentialE]\^\(2\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ y - 68\ \[ExponentialE]\^\(6\ v0 + 4\ y\)\ L\^4\ P\ rm\ rp\ y - 34\ \[ExponentialE]\^v0\ L\^4\ P\ rp\^2\ y + 34\ \[ExponentialE]\^\(5\ v0\)\ L\^4\ P\ rp\^2\ y + 34\ \[ExponentialE]\^\(3\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ y - 34\ \[ExponentialE]\^\(7\ v0 + 4\ y\)\ L\^4\ P\ rp\^2\ \ y)\))\)\) + \(\(1\/\(8\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \ L\)\)\((\[ExponentialE]\^\(-y\)\ t\ \((4\ c2\ \((\(-1\) + \ \[ExponentialE]\^\(2\ v0\))\)\^2\ \((\(-1\) + \[ExponentialE]\^\(2\ y\))\)\ L \ + 4\ c1\ \((\(-1\) + \[ExponentialE]\^\(2\ v0\))\)\^2\ \((1 + \[ExponentialE]\ \^\(2\ y\))\)\ L - \[ExponentialE]\^\(v0/2\)\ P\ \((\[ExponentialE]\^\(3\ v0 \ + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((2 + v0 - 2\ y)\) + \[ExponentialE]\^\(2\ \((v0 + y)\)\)\ \((\ \(-6\) + L\^2\ rm)\)\ \((2 + 3\ v0 - 2\ y)\) + \[ExponentialE]\^\(2\ y\)\ \((\(-6\) + L\^2\ rm)\)\ \((\(-2\) + v0 + 2\ y)\) + \[ExponentialE]\^\(3\ v0\)\ \((\(-6\) + L\^2\ rm)\)\ \((2 + v0 + 2\ y)\) + \[ExponentialE]\^\(v0 + 2\ y\)\ \((6 + L\^2\ rp)\)\ \((\(-2\) + 3\ v0 + 2\ y)\) + \[ExponentialE]\^\(2\ v0\)\ \((6 + L\^2\ rp)\)\ \((2 + 3\ v0 + 2\ y)\) + \((6 + L\^2\ rp)\)\ \((v0 - 2\ \((1 + y)\))\) + \[ExponentialE]\^v0\ \((\(-6\) + L\^2\ rm)\)\ \((3\ v0 - 2\ \((1 + y)\))\))\))\))\)\) + P\ \((1 - \(k\^2\ t\^2\)\/4)\)\ Log[t]\)], "Output"] }, Open ]], Cell[BoxData[""], "Input"], Cell[BoxData[""], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(~\)], "Input"], Cell[BoxData[ \(Syntax::"sntxi" \(\(:\)\(\ \)\) "Incomplete expression; more input is needed.\!\(\"\"\)"\)], "Message"], Cell[BoxData[ StyleBox[ ErrorBox["~"], ShowStringCharacters->True]], "Message"] }, Open ]] }, FrontEndVersion->"4.1 for X", ScreenRectangle->{{0, 1280}, {0, 1024}}, WindowSize->{1027, 1066}, WindowMargins->{{78, Automatic}, {Automatic, 0}}, PrintingPageRange->{Automatic, Automatic}, PrintingOptions->{"PaperSize"->{612, 792}, "PaperOrientation"->"Portrait", "PostScriptOutputFile":>FrontEnd`FileName[{$RootDirectory, "DAMTP", "a", \ "cortex", "local", "raid", "hep", "ajt41", "Mathematica", "5Dpert"}, \ "chiequation.nb.ps", CharacterEncoding -> "ISO8859-1"], "Magnification"->1} ] (******************************************************************* Cached data follows. 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