html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4202.01

 Input Form

 Integrate[Sinh[b Sqrt[z] + d z]^m Cosh[c Sqrt[z] + f z]^v, z] == I^m 2^(-m - v) z Binomial[m, m/2] Binomial[v, v/2] (1 - Mod[m, 2]) (1 - Mod[v, 2]) + 2^(-1 - m - v) Binomial[v, v/2] (1 - Mod[v, 2]) Sum[(-1)^k Binomial[m, k] ((2 E^(b (2 k - m) Sqrt[z] + d (2 k - m) z) (-(-1)^m + E^(2 (-2 k + m) (b Sqrt[z] + d z))))/(d (-2 k + m)) - ((-1)^m b E^((b^2 (-2 k + m))/(4 d)) (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 d (-2 k + m) Sqrt[z])/(2 Sqrt[d (2 k - m)])])/ (d (2 k - m))^(3/2) - (b (-2 k + m) Sqrt[Pi] Erfi[(b (-2 k + m) + 2 d (-2 k + m) Sqrt[z])/ (2 Sqrt[d (-2 k + m)])])/E^((b^2 (-2 k + m))/(4 d))/ (d (-2 k + m))^(3/2)), {k, 0, Floor[(1/2) (-1 + m)]}] - I^m 2^(-1 - m - v) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[v, s] ((2 E^((2 s - v) (c + f Sqrt[z]) Sqrt[z]) (-1 + E^(2 (-2 s + v) (c Sqrt[z] + f z))))/(f (2 s - v)) + (c E^((c^2 (-2 s + v))/(4 f)) Sqrt[Pi] (-2 s + v) Erfi[(c (-2 s + v) + 2 f (-2 s + v) Sqrt[z])/ (2 Sqrt[(-f) (-2 s + v)])])/((-f) (-2 s + v))^(3/2) + (c Sqrt[Pi] (-2 s + v) Erfi[(c (-2 s + v) + 2 f (-2 s + v) Sqrt[z])/ (2 Sqrt[f (-2 s + v)])])/E^((c^2 (-2 s + v))/(4 f))/ (f (-2 s + v))^(3/2)), {s, 0, Floor[(1/2) (-1 + v)]}] + 2^(-1 - m - v) Sum[(-1)^k Binomial[m, k] Sum[Binomial[v, s] ((2 E^(((-b) (2 k - m) - c (-2 s + v)) Sqrt[z] + (d (-2 k + m) - f (-2 s + v)) z))/(d (-2 k + m) - f (-2 s + v)) + (2 (-1)^m E^((b (2 k - m) + c (-2 s + v)) Sqrt[z] + (d (2 k - m) + f (-2 s + v)) z))/ (d (2 k - m) + f (-2 s + v)) - (Sqrt[Pi] (b (2 k - m) + c (-2 s + v)) Erfi[(b (2 k - m) + c (-2 s + v) + 2 (d (2 k - m) + f (-2 s + v)) Sqrt[z])/(2 Sqrt[d (-2 k + m) - f (-2 s + v)])])/ E^(((-b) (2 k - m) - c (-2 s + v))^2/(4 (d (-2 k + m) - f (-2 s + v))))/(d (-2 k + m) - f (-2 s + v))^(3/2) - ((-1)^m Sqrt[Pi] (b (2 k - m) + c (-2 s + v)) Erfi[(b (2 k - m) + c (-2 s + v) + 2 (d (2 k - m) + f (-2 s + v)) Sqrt[z])/(2 Sqrt[d (2 k - m) + f (-2 s + v)])])/ E^((b (2 k - m) + c (-2 s + v))^2/(4 (d (2 k - m) + f (-2 s + v))))/(d (2 k - m) + f (-2 s + v))^(3/2) + (-1)^m ((2 E^(((-b) (-2 k + m) - c (-2 s + v)) Sqrt[z] + (d (2 k - m) - f (-2 s + v)) z))/(d (2 k - m) - f (-2 s + v)) + (2 (-1)^m E^((b (-2 k + m) + c (-2 s + v)) Sqrt[z] + (d (-2 k + m) + f (-2 s + v)) z))/ (d (-2 k + m) + f (-2 s + v)) - (Sqrt[Pi] (b (-2 k + m) + c (-2 s + v)) Erfi[(b (-2 k + m) + c (-2 s + v) + 2 (d (-2 k + m) + f (-2 s + v)) Sqrt[z])/ (2 Sqrt[d (2 k - m) - f (-2 s + v)])])/ E^(((-b) (-2 k + m) - c (-2 s + v))^2/(4 (d (2 k - m) - f (-2 s + v))))/(d (2 k - m) - f (-2 s + v))^(3/2) - ((-1)^m Sqrt[Pi] (b (-2 k + m) + c (-2 s + v)) Erfi[(b (-2 k + m) + c (-2 s + v) + 2 (d (-2 k + m) + f (-2 s + v)) Sqrt[z])/(2 Sqrt[d (-2 k + m) + f (-2 s + v)])])/E^((b (-2 k + m) + c (-2 s + v))^2/(4 (d (-2 k + m) + f (-2 s + v))))/(d (-2 k + m) + f (-2 s + v))^ (3/2))), {s, 0, Floor[(1/2) (-1 + v)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[v, Integers] && v > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]], "m"], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "m"]], "-", "v"]]], " ", "z", " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", "z"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], ")"]]]]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], RowBox[List["4", " ", "d"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], RowBox[List["4", " ", "d"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["f", " ", SqrtBox["z"]]]]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]], ")"]]]]]]], ")"]]]], RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], RowBox[List["4", " ", "f"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], RowBox[List["4", " ", "f"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], ")"]], "/", RowBox[List["(", RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]], ")"]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]]]], ")"]]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]], "\[And]", RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 sinh m ( z b + d z ) cosh v ( z c + f z ) z m 2 - m - v z ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) + 2 - m - v - 1 ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox[FractionBox["v", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 d z ( 2 k - m ) + b z ( 2 k - m ) ( - ( - 1 ) m + 2 ( m - 2 k ) ( z b + d z ) ) d ( m - 2 k ) - ( - 1 ) m b b 2 ( m - 2 k ) 4 d ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 d z ( m - 2 k ) 2 d ( 2 k - m ) ) ( d ( 2 k - m ) ) 3 / 2 - b - b 2 ( m - 2 k ) 4 d ( m - 2 k ) π erfi ( b ( m - 2 k ) + 2 d z ( m - 2 k ) 2 d ( m - 2 k ) ) ( d ( m - 2 k ) ) 3 / 2 ) - m 2 - m - v - 1 ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 ( 2 s - v ) ( c + f z ) z ( - 1 + 2 ( v - 2 s ) ( z c + f z ) ) f ( 2 s - v ) + c c 2 ( v - 2 s ) 4 f π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 f z ( v - 2 s ) 2 - f ( v - 2 s ) ) ( - f ( v - 2 s ) ) 3 / 2 + c - c 2 ( v - 2 s ) 4 f π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 f z ( v - 2 s ) 2 f ( v - 2 s ) ) ( f ( v - 2 s ) ) 3 / 2 ) + 2 - m - v - 1 k = 0 m - 1 2 ( - 1 ) k ( m k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - 1 ) m ( 2 ( - 1 ) m z ( b ( m - 2 k ) + c ( v - 2 s ) ) + ( d ( m - 2 k ) + f ( v - 2 s ) ) z d ( m - 2 k ) + f ( v - 2 s ) - ( ( - 1 ) m - ( b ( m - 2 k ) + c ( v - 2 s ) ) 2 4 ( d ( m - 2 k ) + f ( v - 2 s ) ) π ( b ( m - 2 k ) + c ( v - 2 s ) ) erfi ( b ( m - 2 k ) + c ( v - 2 s ) + 2 ( d ( m - 2 k ) + f ( v - 2 s ) ) z 2 d ( m - 2 k ) + f ( v - 2 s ) ) ) / ( d ( m - 2 k ) + f ( v - 2 s ) ) 3 / 2 + 2 z ( - b ( m - 2 k ) - c ( v - 2 s ) ) + ( d ( 2 k - m ) - f ( v - 2 s ) ) z d ( 2 k - m ) - f ( v - 2 s ) - ( - ( - b ( m - 2 k ) - c ( v - 2 s ) ) 2 4 ( d ( 2 k - m ) - f ( v - 2 s ) ) π ( b ( m - 2 k ) + c ( v - 2 s ) ) erfi ( b ( m - 2 k ) + c ( v - 2 s ) + 2 ( d ( m - 2 k ) + f ( v - 2 s ) ) z 2 d ( 2 k - m ) - f ( v - 2 s ) ) ) / ( d ( 2 k - m ) - f ( v - 2 s ) ) 3 / 2 ) + 2 ( - 1 ) m z ( b ( 2 k - m ) + c ( v - 2 s ) ) + ( d ( 2 k - m ) + f ( v - 2 s ) ) z d ( 2 k - m ) + f ( v - 2 s ) - ( ( - 1 ) m - ( b ( 2 k - m ) + c ( v - 2 s ) ) 2 4 ( d ( 2 k - m ) + f ( v - 2 s ) ) π ( b ( 2 k - m ) + c ( v - 2 s ) ) erfi ( b ( 2 k - m ) + c ( v - 2 s ) + 2 ( d ( 2 k - m ) + f ( v - 2 s ) ) z 2 d ( 2 k - m ) + f ( v - 2 s ) ) ) / ( d ( 2 k - m ) + f ( v - 2 s ) ) 3 / 2 + 2 z ( - b ( 2 k - m ) - c ( v - 2 s ) ) + ( d ( m - 2 k ) - f ( v - 2 s ) ) z d ( m - 2 k ) - f ( v - 2 s ) - ( - ( - b ( 2 k - m ) - c ( v - 2 s ) ) 2 4 ( d ( m - 2 k ) - f ( v - 2 s ) ) π ( b ( 2 k - m ) + c ( v - 2 s ) ) erfi ( b ( 2 k - m ) + c ( v - 2 s ) + 2 ( d ( 2 k - m ) + f ( v - 2 s ) ) z 2 d ( m - 2 k ) - f ( v - 2 s ) ) ) / ( d ( m - 2 k ) - f ( v - 2 s ) ) 3 / 2 ) /; m + v + Condition z z 1 2 b d z m z 1 2 c f z v m 2 -1 m -1 v z Binomial m m 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 2 -1 m -1 v -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 k 0 m -1 2 -1 -1 k Binomial m k 2 d z 2 k -1 m b z 1 2 2 k -1 m -1 -1 m 2 m -1 2 k z 1 2 b d z d m -1 2 k -1 -1 -1 m b b 2 m -1 2 k 4 d -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 d z 1 2 m -1 2 k 2 d 2 k -1 m 1 2 -1 d 2 k -1 m 3 2 -1 -1 b -1 b 2 m -1 2 k 4 d -1 m -1 2 k 1 2 Erfi b m -1 2 k 2 d z 1 2 m -1 2 k 2 d m -1 2 k 1 2 -1 d m -1 2 k 3 2 -1 -1 m 2 -1 m -1 v -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 Binomial v s 2 2 s -1 v c f z 1 2 z 1 2 -1 2 v -1 2 s z 1 2 c f z f 2 s -1 v -1 c c 2 v -1 2 s 4 f -1 1 2 v -1 2 s Erfi c v -1 2 s 2 f z 1 2 v -1 2 s 2 -1 f v -1 2 s 1 2 -1 -1 f v -1 2 s 3 2 -1 c -1 c 2 v -1 2 s 4 f -1 1 2 v -1 2 s Erfi c v -1 2 s 2 f z 1 2 v -1 2 s 2 f v -1 2 s 1 2 -1 f v -1 2 s 3 2 -1 2 -1 m -1 v -1 k 0 m -1 2 -1 -1 k Binomial m k s 0 v -1 2 -1 Binomial v s -1 m 2 -1 m z 1 2 b m -1 2 k c v -1 2 s d m -1 2 k f v -1 2 s z d m -1 2 k f v -1 2 s -1 -1 -1 m -1 b m -1 2 k c v -1 2 s 2 4 d m -1 2 k f v -1 2 s -1 1 2 b m -1 2 k c v -1 2 s Erfi b m -1 2 k c v -1 2 s 2 d m -1 2 k f v -1 2 s z 1 2 2 d m -1 2 k f v -1 2 s 1 2 -1 d m -1 2 k f v -1 2 s 3 2 -1 2 z 1 2 -1 b m -1 2 k -1 c v -1 2 s d 2 k -1 m -1 f v -1 2 s z d 2 k -1 m -1 f v -1 2 s -1 -1 -1 -1 b m -1 2 k -1 c v -1 2 s 2 4 d 2 k -1 m -1 f v -1 2 s -1 1 2 b m -1 2 k c v -1 2 s Erfi b m -1 2 k c v -1 2 s 2 d m -1 2 k f v -1 2 s z 1 2 2 d 2 k -1 m -1 f v -1 2 s 1 2 -1 d 2 k -1 m -1 f v -1 2 s 3 2 -1 2 -1 m z 1 2 b 2 k -1 m c v -1 2 s d 2 k -1 m f v -1 2 s z d 2 k -1 m f v -1 2 s -1 -1 -1 m -1 b 2 k -1 m c v -1 2 s 2 4 d 2 k -1 m f v -1 2 s -1 1 2 b 2 k -1 m c v -1 2 s Erfi b 2 k -1 m c v -1 2 s 2 d 2 k -1 m f v -1 2 s z 1 2 2 d 2 k -1 m f v -1 2 s 1 2 -1 d 2 k -1 m f v -1 2 s 3 2 -1 2 z 1 2 -1 b 2 k -1 m -1 c v -1 2 s d m -1 2 k -1 f v -1 2 s z d m -1 2 k -1 f v -1 2 s -1 -1 -1 -1 b 2 k -1 m -1 c v -1 2 s 2 4 d m -1 2 k -1 f v -1 2 s -1 1 2 b 2 k -1 m c v -1 2 s Erfi b 2 k -1 m c v -1 2 s 2 d 2 k -1 m f v -1 2 s z 1 2 2 d m -1 2 k -1 f v -1 2 s 1 2 -1 d m -1 2 k -1 f v -1 2 s 3 2 -1 m SuperPlus v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]]]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "m"]], "-", "v"]]], " ", "z", " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", "z"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], ")"]]]]]]], ")"]]]], RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", "b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], RowBox[List["4", " ", "d"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], RowBox[List["4", " ", "d"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]], "-", RowBox[List[SuperscriptBox["\[ImaginaryI]", "m"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["f", " ", SqrtBox["z"]]]]], ")"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]], ")"]]]]]]], ")"]]]], RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "s"]], "-", "v"]], ")"]]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], RowBox[List["4", " ", "f"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], RowBox[List["4", " ", "f"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "v"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "-", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "-", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "m"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["d", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]], "&&", RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2002-12-18