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/01.20.21.1299.01

 Input Form

 Integrate[E^(p z) Cos[b z^2]^m Cosh[c z^2], z] == -((1/c) (2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Sqrt[-c] E^(p^2/(4 c)) Erfi[(p - 2 c z)/(2 Sqrt[-c])] - (Sqrt[c] Erfi[(p + 2 c z)/(2 Sqrt[c])])/E^(p^2/(4 c))) (1 - Mod[m, 2]))) + 2^(-2 - m) Sqrt[Pi] Sum[Binomial[m, s] ((((-c + I b m - 2 I b s) Sqrt[c - I b m + 2 I b s] Erfi[(p - 2 (-c + I b m - 2 I b s) z)/(2 Sqrt[c - I b m + 2 I b s])])/E^(p^2/(4 (c - I b m + 2 I b s))) + (Sqrt[-c + I b m - 2 I b s] (c - I b m + 2 I b s) Erfi[(p + 2 (-c + I b m - 2 I b s) z)/(2 Sqrt[-c + I b m - 2 I b s])])/E^(p^2/(4 (-c + I b m - 2 I b s))))/ ((-c + I b m - 2 I b s) (c - I b m + 2 I b s)) + ((Sqrt[c + I b m - 2 I b s] (-c - I b m + 2 I b s) Erfi[(p - 2 (-c - I b m + 2 I b s) z)/(2 Sqrt[c + I b m - 2 I b s])])/E^(p^2/(4 (c + I b m - 2 I b s))) + ((c + I b m - 2 I b s) Sqrt[-c - I b m + 2 I b s] Erfi[(p + 2 (-c - I b m + 2 I b s) z)/(2 Sqrt[-c - I b m + 2 I b s])])/E^(p^2/(4 (-c - I b m + 2 I b s))))/ ((c + I b m - 2 I b s) (-c - I b m + 2 I b s))), {s, 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["Cos", "[", RowBox[List["b", " ", SuperscriptBox["z", "2"]]], "]"]], "m"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", " ", RowBox[List[RowBox[List["-", RowBox[List[FractionBox["1", "c"], RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", "c"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["c"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], ")"]]]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", SqrtBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

 MathML Form

 p z cos m ( b z 2 ) cosh ( c z 2 ) z 2 - m - 2 π s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( - p 2 4 ( - c - b m + 2 b s ) - c - b m + 2 b s ( c + b m - 2 b s ) erfi ( p + 2 ( - c - b m + 2 b s ) z 2 - c - b m + 2 b s ) + - p 2 4 ( c + b m - 2 b s ) ( - c - b m + 2 b s ) c + b m - 2 b s erfi ( p - 2 ( - c - b m + 2 b s ) z 2 c + b m - 2 b s ) ) / ( ( c + b m - 2 b s ) ( - c - b m + 2 b s ) ) + ( - p 2 4 ( c - b m + 2 b s ) c - b m + 2 b s ( - c + b m - 2 b s ) erfi ( p - 2 ( - c + b m - 2 b s ) z 2 c - b m + 2 b s ) + - p 2 4 ( - c + b m - 2 b s ) ( c - b m + 2 b s ) - c + b m - 2 b s erfi ( p + 2 ( - c + b m - 2 b s ) z 2 - c + b m - 2 b s ) ) / ( ( - c + b m - 2 b s ) ( c - b m + 2 b s ) ) ) - 2 - m - 2 π ( 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]]]]] ( - c p 2 4 c erfi ( p - 2 c z 2 - c ) - c - p 2 4 c erfi ( p + 2 c z 2 c ) ) ( 1 - m mod 2 \$CellContext`m 2 ) c /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m > 0 Condition z p z b z 2 m c z 2 2 -1 m -2 1 2 s 0 m -1 2 -1 Binomial m s -1 p 2 4 -1 c -1 b m 2 b s -1 -1 c -1 b m 2 b s 1 2 c b m -1 2 b s Erfi p 2 -1 c -1 b m 2 b s z 2 -1 c -1 b m 2 b s 1 2 -1 -1 p 2 4 c b m -1 2 b s -1 -1 c -1 b m 2 b s c b m -1 2 b s 1 2 Erfi p -1 2 -1 c -1 b m 2 b s z 2 c b m -1 2 b s 1 2 -1 c b m -1 2 b s -1 c -1 b m 2 b s -1 -1 p 2 4 c -1 b m 2 b s -1 c -1 b m 2 b s 1 2 -1 c b m -1 2 b s Erfi p -1 2 -1 c b m -1 2 b s z 2 c -1 b m 2 b s 1 2 -1 -1 p 2 4 -1 c b m -1 2 b s -1 c -1 b m 2 b s -1 c b m -1 2 b s 1 2 Erfi p 2 -1 c b m -1 2 b s z 2 -1 c b m -1 2 b s 1 2 -1 -1 c b m -1 2 b s c -1 b m 2 b s -1 -1 2 -1 m -2 1 2 Binomial m m 2 -1 -1 c 1 2 p 2 4 c -1 Erfi p -1 2 c z 2 -1 c 1 2 -1 -1 c 1 2 -1 p 2 4 c -1 Erfi p 2 c z 2 c 1 2 -1 1 -1 \$CellContext`m 2 c -1 m m 0 [/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["Cos", "[", RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "]"]], "m_"], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List["-", "c"]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["c"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]]]], "c"]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "m"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", SqrtBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", SqrtBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]]]]]], "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]]]], ")"]]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]]]]]]]]]]

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

 2002-12-18