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/01.20.21.1226.01

 Input Form

 Integrate[E^(p z) Sin[b Sqrt[z]]^m Cosh[c Sqrt[z]], z] == 2^(-2 - m) Binomial[m, m/2] ((4 E^(p z) Cosh[c Sqrt[z]])/p + Sqrt[Pi] ((c Erfi[(-c + 2 p Sqrt[z])/(2 Sqrt[p])])/ (E^(c^2/(4 p)) p^(3/2)) - (c 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) ((4 E^((-(1/2)) I m Pi + p z) Cos[(m Pi)/2 + ((-I) c + 2 b k - b m) Sqrt[z]])/p - (1/p^(3/2)) (((c + 2 I b k - I b m) Sqrt[Pi] Erfi[(c + I b (2 k - m) + 2 p Sqrt[z])/(2 Sqrt[p])])/ E^((c + 2 I b k - I b m)^2/(4 p))) - (1/p^(3/2)) (E^(-((-c + I b (-2 k + m))^2/(4 p)) - I m Pi) (-c + I b (-2 k + m)) Sqrt[Pi] Erfi[(-c + I b (-2 k + m) + 2 p Sqrt[z])/(2 Sqrt[p])])) + ((4 E^((I m Pi)/2 + p z) Cos[(m Pi)/2 + (I c + 2 b k - b m) Sqrt[z]])/ p - (1/p^(3/2)) (E^(-((-c + 2 I b k - I b m)^2/(4 p)) + I m Pi) (-c + 2 I b k - I b m) Sqrt[Pi] Erfi[(-c + I b (2 k - m) + 2 p Sqrt[z])/(2 Sqrt[p])]) - (1/p^(3/2)) (((c - 2 I b k + I b m) Sqrt[Pi] Erfi[(c + I b (-2 k + m) + 2 p Sqrt[z])/(2 Sqrt[p])])/E^((c - 2 I b k + I b m)^2/(4 p))))/ 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", " ", SqrtBox["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"], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "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["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", RowBox[List["p", " ", "z"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["m", " ", "\[Pi]"]], "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "p"], "-", RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["p", " ", "z"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["m", " ", "\[Pi]"]], "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "p"], "-", RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", 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 ( π ( c - c 2 4 p erfi ( 2 p z - c 2 p ) p 3 / 2 - c - c 2 4 p erfi ( c + 2 p z 2 p ) p 3 / 2 ) + 4 p z cosh ( c z ) p ) ( 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 ( 4 p z - m π 2 cos ( π m 2 + ( - c + 2 b k - b m ) z ) p - - ( c + 2 b k - b m ) 2 4 p ( c + 2 b k - b m ) π erfi ( c + b ( 2 k - m ) + 2 p z 2 p ) p 3 / 2 - - ( b ( m - 2 k ) - c ) 2 4 p - m π ( b ( m - 2 k ) - c ) π erfi ( - c + b ( m - 2 k ) + 2 p z 2 p ) p 3 / 2 ) + - 1 2 m π ( 4 π m 2 + p z cos ( π m 2 + ( c + 2 b k - b m ) z ) p - 1 p 3 / 2 ( m π - ( - c + 2 b k - b m ) 2 4 p ( - c + 2 b k - b m ) π erfi ( - c + b ( 2 k - m ) + 2 p z 2 p ) ) - - ( c - 2 b k + b m ) 2 4 p ( c - 2 b k + b m ) π erfi ( c + b ( m - 2 k ) + 2 p z 2 p ) p 3 / 2 ) ) /; m + Condition z p z b z 1 2 m c z 1 2 2 -1 m -2 1 2 c -1 c 2 4 p -1 Erfi 2 p z 1 2 -1 c 2 p 1 2 -1 p 3 2 -1 -1 c -1 c 2 4 p -1 Erfi c 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 4 p z c z 1 2 p -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 4 p z -1 m 2 -1 m 2 -1 -1 c 2 b k -1 b m z 1 2 p -1 -1 -1 c 2 b k -1 b m 2 4 p -1 c 2 b k -1 b m 1 2 Erfi c b 2 k -1 m 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 -1 -1 b m -1 2 k -1 c 2 4 p -1 -1 m b m -1 2 k -1 c 1 2 Erfi -1 c b m -1 2 k 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 -1 1 2 m 4 m 2 -1 p z m 2 -1 c 2 b k -1 b m z 1 2 p -1 -1 1 p 3 2 -1 m -1 -1 c 2 b k -1 b m 2 4 p -1 -1 c 2 b k -1 b m 1 2 Erfi -1 c b 2 k -1 m 2 p z 1 2 2 p 1 2 -1 -1 -1 c -1 2 b k b m 2 4 p -1 c -1 2 b k b m 1 2 Erfi c b m -1 2 k 2 p z 1 2 2 p 1 2 -1 p 3 2 -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_", " ", SqrtBox["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"], "+", RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "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["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "+", RowBox[List["p", " ", "z"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["m", " ", "\[Pi]"]], "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "c"]], "+", RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "p"], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "-", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["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["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]], "2"], "+", RowBox[List["p", " ", "z"]]]]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox[RowBox[List["m", " ", "\[Pi]"]], "2"], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", "b", " ", "k"]], "-", RowBox[List["b", " ", "m"]]]], ")"]], " ", SqrtBox["z"]]]]], "]"]]]], "p"], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]], "+", RowBox[List["\[ImaginaryI]", " ", "m", " ", "\[Pi]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "c"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["p", RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["(", RowBox[List["c", "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]]]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], SuperscriptBox["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