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Notebook[{

Cell[CellGroupData[{
Cell[TextData[StyleBox["Nuclear Matter Paper: DR/PDS Equation Checks",
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Cell[TextData[{
  StyleBox["Overview:\nIn this notebook, we check equations for the nuclear \
matter perturbative matching paper and generate numbers for the figures.\nWe \
do dimensional regularization with power divergence subtraction (DR/PDS) \
here.\n\nPlan:\nTry to make the equations and solutions as general as \
possible so that we can expand\n\n",
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  "Write equations as they appear in the notes, using := to define lhs's.  \
Then the evaluation of the rhs is not performed until the lhs is actually \
used somewhere else. This avoids the mess of having explicit arguments for \
everything.\n",
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In order to avoid interference from symbols defined in other \
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Suppress spelling warnings (only do this after the notebook is \
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Cell["Define potentials and find free-space constants", "Section",
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Cell["\<\
Define the forward matrix element of the separable S-wave \
potential:\
\>", "Text",
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  AspectRatioFixed->True],

Cell[BoxData[
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Cell[BoxData[
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Cell["\<\
Since the potential is separable, we can analytically solve for k \
cot \[Delta].\
\>", "Text",
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  AspectRatioFixed->True],

Cell[BoxData[
    \(I0[k_]\  := \ \((k^2 - m^2)\)/\((2  m)\)\)], "Input"],

Cell["\<\
Define the forward K matrix.  We should solve this more generally \
using the CR technology so that we can use different potentials, including \
multiple terms.\
\>", "Text",
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Cell[CellGroupData[{

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Cell["\<\
Match the effective range expansion term-by-term to find \
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\>", "Text",
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Cell["\<\
The a1 result agrees with Appendix (A7) and (A8).
Check various equations in the paper:\
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Cell["\<\
Expand the constants in powers of \[Alpha] and identify the DR/PDS \
perturbative coefficients.\
\>", "Text",
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        RowBox[{
          InterpretationBox[\(O[k]\^5\),
            SeriesData[ k, 0, {}, 5, 5, 1]], " ", "alpha"}], "+", 
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          RowBox[{"(", 
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              RowBox[{\(-\(\(4\ \[ImaginaryI]\ \[Pi]\ k\)\/\(m\^2\ M\)\)\), 
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                InterpretationBox[\(O[k]\^5\),
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                  Power[ M, -1], Pi], 0, 
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                  Power[ M, -1], Pi]}, 1, 5, 1]], ")"}], " ", \(alpha\^2\)}], 
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        InterpretationBox[\(O[alpha]\^3\),
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            Complex[ 0, -4], 
            Power[ m, -2], 
            Power[ M, -1], Pi], 0, 
          Times[ 
            Complex[ 0, 16], 
            Power[ m, -4], 
            Power[ M, -1], Pi]}, 1, 5, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(\(\(\ \)\(vgvpds3\  = \ \ Simplify[
          Series[Series[
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                    C2 \[Rule] C21pds\ alpha\  + \ C22pds\ alpha^2, \ 
                    C4 -> \ C41pds\ alpha\  + \ C42pds\ alpha^2}, {alpha, 0, 
                  2}]\ , \[IndentingNewLine]{p, 0, 4}\ ]\  /. \ 
            p \[Rule] k];\)\)\)], "Input"],

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Cell[BoxData[
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        SeriesData[ k, 0, {
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            Times[ 4, 
              Power[ m, -1], mu]]}, 0, 1, 1]}, 1, 3, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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M\), C42pds \[Rule] \(-\(\(28\ \[Pi]\)\/\(m\^5\ M\)\)\) + \(40\ mu\ \[Pi]\)\/\
\(m\^6\ M\), C41pds \[Rule] \(12\ \[Pi]\)\/\(m\^5\ M\), 
      C21pds \[Rule] \(-\(\(8\ \[Pi]\)\/\(m\^3\ M\)\)\), 
      C01pds \[Rule] \(4\ \[Pi]\)\/\(m\ M\)}\)], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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}, Open  ]],

Cell[CellGroupData[{

Cell["Free Space Error Plots", "Section",
  Evaluatable->False,
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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                      C2 \[Rule] 0, \ C4 -> \ 0}, {alpha, 0, 2}]\ \  /. \ 
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Cell[BoxData[
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                        C01pds\ alpha\  + \ C02pds\ alpha^2, 
                      C2 \[Rule] C21pds\ alpha\  + \ C22pds\ alpha^2, \ 
                      C4 -> \ 0}, {alpha, 0, 2}]\ \  /. \ w2pds\) /. \ 
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Cell[BoxData[
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                        C01pds\ alpha\  + \ C02pds\ alpha^2, 
                      C2 \[Rule] C21pds\ alpha\  + \ C22pds\ alpha^2, \ 
                      C4 -> \ C41pds\ alpha\  + \ C42pds\ alpha^2}, {alpha, 
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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\)], "Output"]
}, Open  ]],

Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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\ \ \ \ \ Evaluate[\(Abs[vgvtrue - vgvDRtot3]*10^6 /. \ 
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\ \ \ \ }, \[IndentingNewLine]{xi,  .001, 
        2}, \[IndentingNewLine]PlotRange \[Rule] {{ .001, 
            1. }, {10^\((\(-8\))\), 10}}, 
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Cell[CellGroupData[{

Cell["Nuclear Matter Energy/A", "Section",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell["\<\
General definitions of dimensionless variable \[Xi] and density 
\
\>", "Text",
  Evaluatable->False,
  AspectRatioFixed->True],

Cell[BoxData[
    \(kf\  := \ xi\ m\)], "Input"],

Cell[BoxData[
    \(rho\  := \ g\ kf^3/\((6\ Pi^2)\)\)], "Input"],

Cell[BoxData[
    \(EoverA\  := \ EoverA1\ \  + \ EoverA2\)], "Input"],

Cell[BoxData[
    \(EoverA1\  := \ g \((g - 1)\)/\((Pi^4\ rho)\)\ m^4\ J\)], "Input"],

Cell[BoxData[
    \(EoverA2\  := \ g \((g - 1)\)/\((Pi^4\ rho)\)\ m^4\ Jp\)], "Input"],

Cell[BoxData[
    \(EoverA2p\  := \ 
      g \((g - 1)\) 
        alpha^2\ m^5/\((6\ Pi^3\ M\ rho)\)\ *\ \((\[IndentingNewLine]\ 
          Log[1 + xi^2]\  - \ 
            xi^2 \((2 + xi^2)\)/\((2\ \((1 + xi^2)\))\)\  - \ 
            Tp1)\)\)], "Input"],

Cell[BoxData[
    \(Tp1\  := \ 
      2/\((35\ Pi)\)\ \((xi^7 \((\(-11\)\  + \ 2  Log[2])\)\  - \ 
            4/9\ xi^9\ \((\(-167\)/3 + 8\ Log[2])\)\ )\)\)], "Input"],

Cell[BoxData[
    \(Jp\  := \ \(\(J1\)\(\ \)\(-\)\(\ \)\(J2\)\(\ \)\)\)], "Input"],

Cell[BoxData[
    \(J\  := \ 
      alpha\ \((2\ Pi\ m/\((3\ M)\))\)\ \((\ 
          xi^2\  + \ 
            xi^3\ ArcTan[
                xi]\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \  - \ \((1\  + \ 
                  3/2\ xi^2)\)\ Log[1 + xi^2]\ )\)\)], "Input"],

Cell[BoxData[
    \(J1\  := \ 
      alpha^2\ \((Pi\ m/\((6\ M)\))\)\ \((Log[1 + xi^2]\  - \ 
            xi^2 \((2 + xi^2)\)/\((2\ \((1 + xi^2)\))\)\ )\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(Series[
      J1/\((alpha^2\ \((Pi\ m/\((6\ M)\))\))\), {xi, 0, 20}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(-\(xi\^6\/6\)\), "+", \(xi\^8\/4\), 
        "-", \(\(3\ xi\^10\)\/10\), "+", \(xi\^12\/3\), 
        "-", \(\(5\ xi\^14\)\/14\), "+", \(\(3\ xi\^16\)\/8\), 
        "-", \(\(7\ xi\^18\)\/18\), "+", \(\(2\ xi\^20\)\/5\), "+", 
        InterpretationBox[\(O[xi]\^21\),
          SeriesData[ xi, 0, {}, 6, 21, 1]]}],
      SeriesData[ xi, 0, {
        Rational[ -1, 6], 0, 
        Rational[ 1, 4], 0, 
        Rational[ -3, 10], 0, 
        Rational[ 1, 3], 0, 
        Rational[ -5, 14], 0, 
        Rational[ 3, 8], 0, 
        Rational[ -7, 18], 0, 
        Rational[ 2, 5]}, 6, 21, 1]]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(J2\  := \ 
      alpha^2 \((m/\((105\ M)\))\)\ \((xi^7 \((\(-11\)\  + \ 
                  2\ Log[2])\)\  - \ 
            4/9\ xi^9\ \((\(-167\)/3\  + \ 8  Log[2])\)\ )\)\)], "Input"],

Cell[BoxData[
    \(EoverApds\  := \ EoverA1pds\  + \ EoverA2ppds\)], "Input"],

Cell[BoxData[
    \(EoverA1pds\  := \ \((g - 1)\) 
        alpha\ \((m^2/\((3\ Pi\ M)\))\)\ \((M\ m/\((4\ Pi)\))\)\ *\ \((\
\[IndentingNewLine]\ \ C01p\ xi^3\  + \ 3/10\ m^2\ C21p\ xi^5\  + \ 
            9/70\ m^4\ C41p\ xi^7\ )\)\)], "Input"],

Cell[BoxData[
    \(EoverA2ppds\  := \ 
      g \((g - 1)\) 
        alpha^2\ m^5/\((6\ Pi^3\ M\ rho)\)\ *\((\[IndentingNewLine]\ \ \
\((M/\((4\ Pi\ m)\))\)^2\ \((\ 
              16\ Pi\ m/M\ Apds\  - \ mu/m\ Bpds\  - 
                Tptilde\ )\)\ )\)\)], "Input"],

Cell[BoxData[
    \(EoverA2pds\  := \ \(-\((g - 
              1)\)\)\ alpha^2\ m^2\ /\ \((6\ Pi\ M)\)\ *\ \((M\ m/\((4\ \
Pi)\))\)\ *\[IndentingNewLine]\((\ \((\(-2\)\ C02p\  + \ 
                  M\ mu/\((2\ Pi)\)\ C01p^2)\)\ xi^3\  - \ 
            3\ m\ M\ C01p^2\ \((11\  - \ 
                    2\ Log[2])\)/\((35\ Pi^2)\)\ xi^4\[IndentingNewLine]\  - \
\ \((3/5\ C22p\  - \ 
                  3/\((10\ Pi)\)\ M\ mu\ C01p\ C21p)\)\ m^2\ xi^5\
\[IndentingNewLine] - \ 
            C01p\ C21p\ M\ m^3\ 2\ \((167/3\  - \ 
                    8\ Log[2])\)/\((105\ Pi^2)\)\ xi^6\[IndentingNewLine] - \ \
\((9/35\ C42p\  - \ 
                  9/\((140\ Pi)\)\ M\ mu\ \((\ 
                      C21p^2\  + \ 
                        2  C01p\ C41p)\))\)\ m^4\ xi^7\ )\)\)], "Input"],

Cell[BoxData[
    \(Apds\  := \ 
      xi^6/12\ m^2\ C02p\  + \ xi^8/40\ m^4\ C22p\  + \ 
        3\ xi^10/280\ m^6\ C42p\)], "Input"],

Cell[BoxData[
    \(Bpds\  := \ 
      xi^6/3 \((m^2\ C01p)\)^2\  + \ xi^8/5\ m^6\ C01p\ C21p\  + \ 
        3/70\ xi^10\ \((\ \((m^4\ C21p)\)^2\  + \ 
              2\ m^8\ C01p\ C41p\ )\)\)], "Input"],

Cell[BoxData[
    \(Tptilde\  := \ 
      2/\((35\ Pi)\)\ \((xi^7 \((m^2\ C01p)\)^2\ \((\(-11\)\  + \ 
                  2  Log[2])\)\  + \ 
            2/9\ xi^9\ \ m^6\ C01p\ C21p \((\(-167\)/3 + 
                  8\ Log[2])\)\ )\)\)], "Input"],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf1\  = \ 
      Series[EoverA1, {xi, 0, 15}]/\((\ \((g - 1)\) 
            alpha\ m^2/\((3\ Pi\ M)\)\ )\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), "-", \(\(3\ xi\^5\)\/5\), "+", \(\(27\ xi\^7\)\/70\),
         "-", \(\(4\ xi\^9\)\/15\), "+", \(\(15\ xi\^11\)\/77\), 
        "-", \(\(27\ xi\^13\)\/182\), "+", \(\(7\ xi\^15\)\/60\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
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        Rational[ -3, 5], 0, 
        Rational[ 27, 70], 0, 
        Rational[ -4, 15], 0, 
        Rational[ 15, 77], 0, 
        Rational[ -27, 182], 0, 
        Rational[ 7, 60]}, 3, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf2\  = \ 
      Series[EoverA1pds, {xi, 0, 15}]/\((\ \((g - 1)\) 
            alpha\ m^2/\((3\ Pi\ M)\)\ )\)\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(C01p\ m\ M\ xi\^3\)\/\(4\ \[Pi]\)\), 
        "+", \(\(3\ C21p\ m\^3\ M\ xi\^5\)\/\(40\ \[Pi]\)\), 
        "+", \(\(9\ C41p\ m\^5\ M\ xi\^7\)\/\(280\ \[Pi]\)\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 3, 16, 1]]}],
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          Power[ Pi, -1]], 0, 
        Times[ 
          Rational[ 3, 40], C21p, 
          Power[ m, 3], M, 
          Power[ Pi, -1]], 0, 
        Times[ 
          Rational[ 9, 280], C41p, 
          Power[ m, 5], M, 
          Power[ Pi, -1]]}, 3, 16, 1]]], "Output"]
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Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\ 
      sf1 - sf2\  /. \ {C01p \[Rule] C01, C21p \[Rule] 0, 
          C41p \[Rule] 0}]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(-\(\(3\ xi\^5\)\/5\)\), "+", \(\(27\ xi\^7\)\/70\), 
        "-", \(\(4\ xi\^9\)\/15\), "+", \(\(15\ xi\^11\)\/77\), 
        "-", \(\(27\ xi\^13\)\/182\), "+", \(\(7\ xi\^15\)\/60\), "+", 
        InterpretationBox[\(O[xi]\^16\),
          SeriesData[ xi, 0, {}, 5, 16, 1]]}],
      SeriesData[ xi, 0, {
        Rational[ -3, 5], 0, 
        Rational[ 27, 70], 0, 
        Rational[ -4, 15], 0, 
        Rational[ 15, 77], 0, 
        Rational[ -27, 182], 0, 
        Rational[ 7, 60]}, 5, 16, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf3\  = \ 
      Simplify[Series[
            EoverA2, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ xi\^5\)\/2\), 
        "-", \(\(16\ \((\(-167\) + 24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\)\), 
        "+", \(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Rational[ -3, 2], 
        Times[ 
          Rational[ -16, 315], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Rational[ 9, 5], 0, -2}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf3p = \ 
      Simplify[Series[
            EoverA2p, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(xi\^3\), 
        "+", \(\(12\ \((\(-11\) + Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\)\), 
        "-", \(\(3\ xi\^5\)\/2\), 
        "-", \(\(16\ \((\(-167\) + 24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\)\), 
        "+", \(\(9\ xi\^7\)\/5\), "-", \(2\ xi\^9\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {1, 
        Times[ 
          Rational[ 12, 35], 
          Power[ Pi, -1], 
          Plus[ -11, 
            Log[ 4]]], 
        Rational[ -3, 2], 
        Times[ 
          Rational[ -16, 315], 
          Power[ Pi, -1], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Rational[ 9, 5], 0, -2}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[sf3 - sf3p]\)], "Input"],

Cell[BoxData[
    InterpretationBox[\(O[xi]\^10\),
      SeriesData[ xi, 0, {}, 10, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf4 = \ 
      Simplify[Series[
            EoverA2pds, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(m\ M\ \((C01p\^2\ M\ mu - 
                  4\ C02p\ \[Pi])\)\ xi\^3\)\/\(8\ \[Pi]\^2\)\), 
        "+", \(\(3\ C01p\^2\ m\^2\ M\^2\ \((\(-11\) + 
                  Log[4])\)\ xi\^4\)\/\(140\ \[Pi]\^3\)\), 
        "+", \(\(3\ m\^3\ M\ \((C01p\ C21p\ M\ mu - 
                  2\ C22p\ \[Pi])\)\ xi\^5\)\/\(40\ \[Pi]\^2\)\), 
        "+", \(\(C01p\ C21p\ m\^4\ M\^2\ \((\(-167\) + 
                  24\ Log[2])\)\ xi\^6\)\/\(630\ \[Pi]\^3\)\), 
        "+", \(\(9\ m\^5\ M\ \((C21p\^2\ M\ mu + 2\ C01p\ C41p\ M\ mu - 
                  4\ C42p\ \[Pi])\)\ xi\^7\)\/\(560\ \[Pi]\^2\)\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {
        Times[ 
          Rational[ 1, 8], m, M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ 
              Power[ C01p, 2], M, mu], 
            Times[ -4, C02p, Pi]]], 
        Times[ 
          Rational[ 3, 140], 
          Power[ C01p, 2], 
          Power[ m, 2], 
          Power[ M, 2], 
          Power[ Pi, -3], 
          Plus[ -11, 
            Log[ 4]]], 
        Times[ 
          Rational[ 3, 40], 
          Power[ m, 3], M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ C01p, C21p, M, mu], 
            Times[ -2, C22p, Pi]]], 
        Times[ 
          Rational[ 1, 630], C01p, C21p, 
          Power[ m, 4], 
          Power[ M, 2], 
          Power[ Pi, -3], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Times[ 
          Rational[ 9, 560], 
          Power[ m, 5], M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ 
              Power[ C21p, 2], M, mu], 
            Times[ 2, C01p, C41p, M, mu], 
            Times[ -4, C42p, Pi]]]}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(sf4p = \ 
      Simplify[Series[
            EoverA2ppds, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)]\)], "Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\(m\ M\ \((C01p\^2\ M\ mu - 
                  4\ C02p\ \[Pi])\)\ xi\^3\)\/\(8\ \[Pi]\^2\)\), 
        "+", \(\(3\ C01p\^2\ m\^2\ M\^2\ \((\(-11\) + 
                  Log[4])\)\ xi\^4\)\/\(140\ \[Pi]\^3\)\), 
        "+", \(\(3\ m\^3\ M\ \((C01p\ C21p\ M\ mu - 
                  2\ C22p\ \[Pi])\)\ xi\^5\)\/\(40\ \[Pi]\^2\)\), 
        "+", \(\(C01p\ C21p\ m\^4\ M\^2\ \((\(-167\) + 
                  24\ Log[2])\)\ xi\^6\)\/\(630\ \[Pi]\^3\)\), 
        "+", \(\(9\ m\^5\ M\ \((C21p\^2\ M\ mu + 2\ C01p\ C41p\ M\ mu - 
                  4\ C42p\ \[Pi])\)\ xi\^7\)\/\(560\ \[Pi]\^2\)\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {
        Times[ 
          Rational[ 1, 8], m, M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ 
              Power[ C01p, 2], M, mu], 
            Times[ -4, C02p, Pi]]], 
        Times[ 
          Rational[ 3, 140], 
          Power[ C01p, 2], 
          Power[ m, 2], 
          Power[ M, 2], 
          Power[ Pi, -3], 
          Plus[ -11, 
            Log[ 4]]], 
        Times[ 
          Rational[ 3, 40], 
          Power[ m, 3], M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ C01p, C21p, M, mu], 
            Times[ -2, C22p, Pi]]], 
        Times[ 
          Rational[ 1, 630], C01p, C21p, 
          Power[ m, 4], 
          Power[ M, 2], 
          Power[ Pi, -3], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Times[ 
          Rational[ 9, 560], 
          Power[ m, 5], M, 
          Power[ Pi, -2], 
          Plus[ 
            Times[ 
              Power[ C21p, 2], M, mu], 
            Times[ 2, C01p, C41p, M, mu], 
            Times[ -4, C42p, Pi]]]}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[\(Series[
            EoverA2ppds, {xi, 0, 9}]/\((\(-\((g - 1)\)\) 
              alpha^2\ m^2/\((6\ Pi\ M)\))\)\)/\((M\ m/\((4\ Pi)\))\)]\)], \
"Input"],

Cell[BoxData[
    InterpretationBox[
      RowBox[{\(\((\(-2\)\ C02p + \(C01p\^2\ M\ mu\)\/\(2\ \[Pi]\))\)\ \
xi\^3\), "+", \(\(3\ C01p\^2\ m\ M\ \((\(-11\) + 
                  Log[4])\)\ xi\^4\)\/\(35\ \[Pi]\^2\)\), 
        "+", \(\(3\ m\^2\ \((C01p\ C21p\ M\ mu - 
                  2\ C22p\ \[Pi])\)\ xi\^5\)\/\(10\ \[Pi]\)\), 
        "+", \(\(2\ C01p\ C21p\ m\^3\ M\ \((\(-167\) + 
                  24\ Log[2])\)\ xi\^6\)\/\(315\ \[Pi]\^2\)\), 
        "+", \(\(9\ m\^4\ \((C21p\^2\ M\ mu + 2\ C01p\ C41p\ M\ mu - 
                  4\ C42p\ \[Pi])\)\ xi\^7\)\/\(140\ \[Pi]\)\), "+", 
        InterpretationBox[\(O[xi]\^10\),
          SeriesData[ xi, 0, {}, 3, 10, 1]]}],
      SeriesData[ xi, 0, {
        Plus[ 
          Times[ -2, C02p], 
          Times[ 
            Rational[ 1, 2], 
            Power[ C01p, 2], M, mu, 
            Power[ Pi, -1]]], 
        Times[ 
          Rational[ 3, 35], 
          Power[ C01p, 2], m, M, 
          Power[ Pi, -2], 
          Plus[ -11, 
            Log[ 4]]], 
        Times[ 
          Rational[ 3, 10], 
          Power[ m, 2], 
          Power[ Pi, -1], 
          Plus[ 
            Times[ C01p, C21p, M, mu], 
            Times[ -2, C22p, Pi]]], 
        Times[ 
          Rational[ 2, 315], C01p, C21p, 
          Power[ m, 3], M, 
          Power[ Pi, -2], 
          Plus[ -167, 
            Times[ 24, 
              Log[ 2]]]], 
        Times[ 
          Rational[ 9, 140], 
          Power[ m, 4], 
          Power[ Pi, -1], 
          Plus[ 
            Times[ 
              Power[ C21p, 2], M, mu], 
            Times[ 2, C01p, C41p, M, mu], 
            Times[ -4, C42p, Pi]]]}, 3, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
    \(Simplify[sf4 - sf4p]\)], "Input"],

Cell[BoxData[
    InterpretationBox[\(O[xi]\^10\),
      SeriesData[ xi, 0, {}, 10, 10, 1]]], "Output"]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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                imax}]\  /. \ {C01p \[Rule] C01, C02p \[Rule] C02, 
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Cell[BoxData[
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Cell[BoxData[
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Cell[BoxData[
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Cell[CellGroupData[{

Cell[BoxData[
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Cell[BoxData[
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  ImageRangeCache->{{{91.5625, 415.625}, {349.688, 149.75}} -> {-1.4231, \
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Cell[BoxData[
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      False,
      Editable->False]], "Output"]
}, Open  ]],

Cell[BoxData[
    \(ximin\  = \  .001; \ \ ximax\  = \ 2; \ \ delxi\  = \ 1.2;\)], "Input"],

Cell[BoxData[
    \(xip[i_]\  := \ ximin\ delxi^i\)], "Input"],

Cell[BoxData[
    \(maxt1[xip_]\  := \(Abs[factor*sfmaxt1[11]] /. parameters\)\  /. \ 
        xi \[Rule] xip\)], "Input"],

Cell[BoxData[
    \(maxt2[xip_]\  := \(Abs[factor*sfmaxt2[11]] /. parameters\)\  /. \ 
        xi \[Rule] xip\)], "Input"],

Cell[BoxData[
    \(maxt3[xip_]\  := \(Abs[factor*sfmaxt3[11]] /. parameters\)\  /. \ 
        xi \[Rule] xip\)], "Input"],

Cell["\<\
To extract this table for use in xmgr or xmgrace, first select it \
(clicking on the bar on the right) and then do Cell->Convert to OutputForm.  \
This gets rid of spaces in the exponent.  Then do Edit->Copy As Plain Text, \
which puts it in the copy buffer.  Open up a new nedit window
or emacs window and you should be able to just \"paste\" the result in \
(ctrl-v or Paste from the Edit menu in Nedit).\
\>", "Text"],

Cell[CellGroupData[{

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FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(Abs[
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              xi \[Rule] 
                xip[i]], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(Abs[
                  factor*sfmaxt2[11]] /. parameters\) /. \ 
              xi \[Rule] 
                xip[i]], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ FortranForm[\[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \(Abs[
                  factor*sfmaxt3[11]] /. parameters\) /. \ 
              xi \[Rule] 
                xip[i]]}, \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ {i, 0, 
          Log[ximax/ximin]/
            Log[delxi]}], \[IndentingNewLine]\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\ \ \ \ \ TableSpacing \[Rule] {0, 1}]\)\)\)], "Input"],

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