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/01.20.21.4058.01

 Input Form

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

 Standard Form

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

 MathML Form

 sinh ( z b + d z ) cosh v ( g + f z ) z 2 - v - 2 ( 4 cosh ( z b + d z ) d + b b 2 4 d π erfi ( b + 2 d z 2 - d ) ( - d ) 3 / 2 - b - b 2 4 d π erfi ( b + 2 d z 2 d ) d 3 / 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 - v mod 2 \$CellContext`v 2 ) + 2 - v - 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]]]]] ( - g ( v - 2 s ) ( 4 g ( v - 2 s ) cosh ( z b + d z + ( 2 s - v ) ( g + f z ) ) d + 2 f s - f v + b - b 2 4 ( d - f ( v - 2 s ) ) π erfi ( 2 ( f ( v - 2 s ) - d ) z - b 2 d - f ( v - 2 s ) ) ( d - f ( v - 2 s ) ) 3 / 2 - b 2 g ( v - 2 s ) - b 2 4 ( f ( v - 2 s ) - d ) π erfi ( 2 ( f ( v - 2 s ) - d ) z - b 2 f ( v - 2 s ) - d ) ( f ( v - 2 s ) - d ) 3 / 2 ) - - g ( v - 2 s ) ( - 4 g ( v - 2 s ) cosh ( z b + d z - ( 2 s - v ) ( g + f z ) ) d + f ( v - 2 s ) + b 2 g ( v - 2 s ) - b 2 4 ( d + f ( v - 2 s ) ) π erfi ( b + 2 ( d + f ( v - 2 s ) ) z 2 d + f ( v - 2 s ) ) ( d + f ( v - 2 s ) ) 3 / 2 - b - b 2 4 ( - d - f ( v - 2 s ) ) π erfi ( b + 2 ( d + f ( v - 2 s ) ) z 2 - d - f ( v - 2 s ) ) ( - d - f ( v - 2 s ) ) 3 / 2 ) ) /; v + Condition z z 1 2 b d z g f z v 2 -1 v -2 4 z 1 2 b d z d -1 b b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 b -1 b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 s 0 v -1 2 -1 Binomial v s -1 g v -1 2 s 4 g v -1 2 s z 1 2 b d z 2 s -1 v g f z d 2 f s -1 f v -1 b -1 b 2 4 d -1 f v -1 2 s -1 1 2 Erfi 2 f v -1 2 s -1 d z 1 2 -1 b 2 d -1 f v -1 2 s 1 2 -1 d -1 f v -1 2 s 3 2 -1 -1 b 2 g v -1 2 s -1 b 2 4 f v -1 2 s -1 d -1 1 2 Erfi 2 f v -1 2 s -1 d z 1 2 -1 b 2 f v -1 2 s -1 d 1 2 -1 f v -1 2 s -1 d 3 2 -1 -1 -1 g v -1 2 s -1 4 g v -1 2 s z 1 2 b d z -1 2 s -1 v g f z d f v -1 2 s -1 b 2 g v -1 2 s -1 b 2 4 d f v -1 2 s -1 1 2 Erfi b 2 d f v -1 2 s z 1 2 2 d f v -1 2 s 1 2 -1 d f v -1 2 s 3 2 -1 -1 b -1 b 2 4 -1 d -1 f v -1 2 s -1 1 2 Erfi b 2 d f v -1 2 s z 1 2 2 -1 d -1 f v -1 2 s 1 2 -1 -1 d -1 f v -1 2 s 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

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

 2002-12-18