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/01.20.21.1222.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], "m"], RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]]]], "p"], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", 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[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "m", " ", "\[Pi]"]], "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z sin m ( b z ) cosh ( c z ) z 2 - m - 2 ( 4 p z cosh ( c z ) p - c - c 2 4 p π ( erfi ( c + 2 p z 2 p ) - erfi ( 2 p z - c 2 p ) ) p 3 / 2 ) ( 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 ) + 2 - m - 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]]]]] ( m π 2 ( c - c 2 4 ( - 2 b k + b m + p ) - m π π erfi ( 2 ( - 2 b k + b m + p ) z - c 2 - 2 b k + b m + p ) ( - 2 b k + b m + p ) 3 / 2 + 2 - z c + ( - 2 b k + b m + p ) z - m π - 2 b k + b m + p + 2 z c + ( 2 b k - b m + p ) z 2 b k - b m + p - c - c 2 4 ( 2 b k - b m + p ) π erfi ( c + 2 ( 2 b k - b m + p ) z 2 2 b k - b m + p ) ( 2 b k - b m + p ) 3 / 2 ) + - 1 2 m π ( - c - c 2 4 ( - 2 b k + b m + p ) π erfi ( c + 2 ( - 2 b k + b m + p ) z 2 - 2 b k + b m + p ) ( - 2 b k + b m + p ) 3 / 2 + c m π - c 2 4 ( 2 b k - b m + p ) π erfi ( 2 ( 2 b k - b m + p ) z - c 2 2 b k - b m + p ) ( 2 b k - b m + p ) 3 / 2 + 2 z c + ( - 2 b k + b m + p ) z - 2 b k + b m + p + 2 - z c + ( 2 b k - b m + p ) z + m π 2 b k - b m + p ) ) /; m + Condition z p z b z m c z 1 2 2 -1 m -2 4 p z c z 1 2 p -1 -1 c -1 c 2 4 p -1 1 2 Erfi c 2 p z 1 2 2 p 1 2 -1 -1 Erfi 2 p z 1 2 -1 c 2 p 1 2 -1 p 3 2 -1 Binomial m m 2 -1 1 -1 \$CellContext`m 2 2 -1 m -2 k 0 m -1 2 -1 -1 k Binomial m k m 2 -1 c -1 c 2 4 -2 b k b m p -1 -1 m 1 2 Erfi 2 -2 b k b m p z 1 2 -1 c 2 -2 b k b m p 1 2 -1 -2 b k b m p 3 2 -1 2 -1 z 1 2 c -2 b k b m p z -1 m -2 b k b m p -1 2 z 1 2 c 2 b k -1 b m p z 2 b k -1 b m p -1 -1 c -1 c 2 4 2 b k -1 b m p -1 1 2 Erfi c 2 2 b k -1 b m p z 1 2 2 2 b k -1 b m p 1 2 -1 2 b k -1 b m p 3 2 -1 -1 1 2 m -1 c -1 c 2 4 -2 b k b m p -1 1 2 Erfi c 2 -2 b k b m p z 1 2 2 -2 b k b m p 1 2 -1 -2 b k b m p 3 2 -1 c m -1 c 2 4 2 b k -1 b m p -1 1 2 Erfi 2 2 b k -1 b m p z 1 2 -1 c 2 2 b k -1 b m p 1 2 -1 2 b k -1 b m p 3 2 -1 2 z 1 2 c -2 b k b m p z -2 b k b m p -1 2 -1 z 1 2 c 2 b k -1 b m p z m 2 b k -1 b m p -1 m SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", "z_"]]], " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], "m_"], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]]]], "p"], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", 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[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "m", " ", "\[Pi]"]], "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]]]]]]]]]]

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

 2002-12-18