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/01.20.21.3840.01

 Input Form

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

 p z 2 cos m ( b z ) cosh v ( c z ) z 2 - m - v - 1 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]]]]] ( 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]]]]] erfi ( p z ) ( 1 - m mod 2 \$CellContext`m 2 ) ( 1 - v mod 2 \$CellContext`v 2 ) p + 1 p ( 2 - m - v - 1 π ( 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 ) s = 0 m - 1 2 b 2 ( m - 2 s ) 2 4 p ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( erfi ( 2 p z - b ( m - 2 s ) 2 p ) + erfi ( b ( m - 2 s ) + 2 p z 2 p ) ) ) + 1 p ( 2 - m - v - 1 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]]]]] ( 1 - m mod 2 \$CellContext`m 2 ) s = 0 v - 1 2 - c 2 ( v - 2 s ) 2 4 p ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( erfi ( 2 p z - c ( v - 2 s ) 2 p ) + erfi ( c ( v - 2 s ) + 2 p z 2 p ) ) ) + 1 p ( 2 - m - v - 1 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]]]]] k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( - 2 c k - b m + 2 b s + c v ) 2 4 p erfi ( - 2 c k - b m + 2 b s + c v + 2 p z 2 p ) + - ( - 2 c k + b m - 2 b s + c v ) 2 4 p erfi ( - 2 c k + b m - 2 b s + c v + 2 p z 2 p ) + - ( 2 c k - b m + 2 b s - c v ) 2 4 p erfi ( 2 c k - b m + 2 b s - c v + 2 p z 2 p ) + - ( 2 c k + b m - 2 b s - c v ) 2 4 p erfi ( 2 c k + b m - 2 b s - c v + 2 p z 2 p ) ) ) /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m > 0 v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z p z 2 b z m c z v 2 -1 m -1 v -1 1 2 Binomial m m 2 -1 Binomial v v 2 -1 Erfi p 1 2 z 1 -1 \$CellContext`m 2 1 -1 \$CellContext`v 2 p 1 2 -1 1 p 1 2 -1 2 -1 m -1 v -1 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 s 0 m -1 2 -1 b 2 m -1 2 s 2 4 p -1 Binomial m s Erfi 2 p z -1 b m -1 2 s 2 p 1 2 -1 Erfi b m -1 2 s 2 p z 2 p 1 2 -1 1 p 1 2 -1 2 -1 m -1 v -1 1 2 Binomial m m 2 -1 1 -1 \$CellContext`m 2 s 0 v -1 2 -1 -1 c 2 v -1 2 s 2 4 p -1 Binomial v s Erfi 2 p z -1 c v -1 2 s 2 p 1 2 -1 Erfi c v -1 2 s 2 p z 2 p 1 2 -1 1 p 1 2 -1 2 -1 m -1 v -1 1 2 s 0 m -1 2 -1 Binomial m s k 0 v -1 2 -1 Binomial v k -1 -2 c k -1 b m 2 b s c v 2 4 p -1 Erfi -2 c k -1 b m 2 b s c v 2 p z 2 p 1 2 -1 -1 -2 c k b m -1 2 b s c v 2 4 p -1 Erfi -2 c k b m -1 2 b s c v 2 p z 2 p 1 2 -1 -1 2 c k -1 b m 2 b s -1 c v 2 4 p -1 Erfi 2 c k -1 b m 2 b s -1 c v 2 p z 2 p 1 2 -1 -1 2 c k b m -1 2 b s -1 c v 2 4 p -1 Erfi 2 c k b m -1 2 b s -1 c v 2 p z 2 p 1 2 -1 m m 0 v v 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SuperscriptBox["z_", "2"]]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], "m_"], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["p"], " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], SqrtBox["p"]], "+", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", SqrtBox["\[Pi]"], " ", 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["s", "=", "0"]], RowBox[List["Floor", "[", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "m"]], ")"]]]], "]"]]], RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]], "2"]]], RowBox[List["4", " ", "p"]]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List["m", "-", RowBox[List["2", " ", "s"]]]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]]]]]], SqrtBox["p"]], "+", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", SqrtBox["\[Pi]"], " ", 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[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["c", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], "2"]]], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", "s"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]], "+", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], ")"]]]]]]]], SqrtBox["p"]], "+", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "-", "m", "-", "v"]]], " ", 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[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "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", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["2", " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "-", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "+", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "+", RowBox[List["c", " ", "v"]]]], ")"]], "2"], RowBox[List["4", " ", "p"]]]]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "c", " ", "k"]], "-", RowBox[List["\[ImaginaryI]", " ", "b", " ", "m"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b", " ", "s"]], "+", RowBox[List["c", " ", "v"]], "+", RowBox[List["2", " ", "p", " ", "z"]]]], RowBox[List["2", " ", SqrtBox["p"]]]], "]"]]]]]], ")"]]]]]]]]]]]], SqrtBox["p"]]]], "/;", 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