Integrate[E^(p Sqrt[z]) Cos[b Sqrt[z]]^m Cosh[c z], z] == (Binomial[m, m/2] (1 - Mod[m, 2]) ((((p Sqrt[Pi])/(4 c^(3/2))) (E^(p^2/(2 c)) Erf[(-p + 2 c Sqrt[z])/(2 Sqrt[c])] - Erfi[(p + 2 c Sqrt[z])/(2 Sqrt[c])]))/E^(p^2/(4 c)) + (E^(p Sqrt[z]) Sinh[c z])/c))/2^m + 2^(-2 - m) Sum[Binomial[m, k] ((8 E^(p Sqrt[z]) Cos[b (2 k - m) Sqrt[z]] Sinh[c z])/c + (1/(-c)^(5/2)) (c E^(((-I) b (-2 k + m) + p)^2/(4 c)) ((-I) b (-2 k + m) + p) Sqrt[Pi] Erfi[((-I) b (-2 k + m) + p - 2 c Sqrt[z])/(2 Sqrt[-c])]) + (1/(-c)^(5/2)) (c E^((I b (-2 k + m) + p)^2/(4 c)) (I b (-2 k + m) + p) Sqrt[Pi] Erfi[(I b (-2 k + m) + p - 2 c Sqrt[z])/(2 Sqrt[-c])]) - (1/c^(3/2)) (E^((b (-2 k + m) + I p)^2/(4 c)) ((-I) b (-2 k + m) + p) Sqrt[Pi] Erfi[((-I) b (-2 k + m) + p + 2 c Sqrt[z])/(2 Sqrt[c])]) - (1/c^(3/2)) (((I b (-2 k + m) + p) Sqrt[Pi] Erfi[(I b (-2 k + m) + p + 2 c Sqrt[z])/(2 Sqrt[c])])/ E^((I b (-2 k + m) + p)^2/(4 c)))), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], "m"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["-", "m"]]], RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List["p", " ", SqrtBox["\[Pi]"], " "]], RowBox[List["4", " ", SuperscriptBox["c", RowBox[List["3", "/", "2"]]]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["2", " ", "c"]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "p"]], "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], "-", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], ")"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "c"]]], ")"]]]], "+", 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[RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "c"], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["5", "/", "2"]]]], RowBox[List["(", RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["5", "/", "2"]]]], RowBox[List["(", RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["c", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], ")"]]]], "-", RowBox[List[FractionBox["1", SuperscriptBox["c", RowBox[List["3", "/", "2"]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], ")"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "\[And]", RowBox[List["m", ">", "0"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> p </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mi> m </mi> </msup> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <msup> <mn> 2 </mn> <mrow> <mo> - </mo> <mi> m </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mrow> <mi> p </mi> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> </mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> c </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <msup> <mi> p </mi> <mn> 2 </mn> </msup> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mi> erf </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> c </mi> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> c </mi> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> p </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> c </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mfrac> <mi> m </mi> <mn> 2 </mn> </mfrac> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[FractionBox[&quot;m&quot;, &quot;2&quot;], Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <semantics> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mi> mod </mi> <mo> &#8290; </mo> <mn> 2 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mn> 2 </mn> <mrow> <mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <semantics> <mrow> <mo> ( </mo> <mtable> <mtr> <mtd> <mi> m </mi> </mtd> </mtr> <mtr> <mtd> <mi> k </mi> </mtd> </mtr> </mtable> <mo> ) </mo> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;(&quot;, GridBox[List[List[TagBox[&quot;m&quot;, Identity]], List[TagBox[&quot;k&quot;, Identity]]]], &quot;)&quot;]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] </annotation> </semantics> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mi> c </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> c </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mi> c </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> p </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> c </mi> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mi> c </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> &#960; </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> erfi </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> p </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mi> c </mi> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <msup> <mi> c </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> + </mo> <mfrac> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> p </mi> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mi> c </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> m </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> m </ci> </apply> <apply> <cosh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <ci> p </ci> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <ci> p </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </uplimit> <apply> <times /> <apply> <ci> Binomial </ci> <ci> m </ci> <ci> k </ci> </apply> <apply> <plus /> <apply> <times /> <ci> c </ci> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> c </ci> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> c </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> c </ci> </apply> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> </apply> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> c </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <ci> p </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <cos /> <apply> <times /> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SqrtBox["z_"]]]], " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["b_", " ", SqrtBox["z_"]]], "]"]], "m_"], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["-", "m"]]], " ", RowBox[List["Binomial", "[", RowBox[List["m", ",", FractionBox["m", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["m", ",", "2"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["p", " ", SqrtBox["\[Pi]"]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["2", " ", "c"]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List[RowBox[List["-", "p"]], "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], "-", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], ")"]]]], RowBox[List["4", " ", SuperscriptBox["c", RowBox[List["3", "/", "2"]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "c"]]], ")"]]]], "+", 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[RowBox[List["Binomial", "[", RowBox[List["m", ",", "k"]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]], ")"]], " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "c"], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["5", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "-", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "c"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "c"]], ")"]], RowBox[List["5", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], ")"]], "2"], RowBox[List["4", " ", "c"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], SuperscriptBox["c", RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], "2"], RowBox[List["4", " ", "c"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p"]], ")"]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "m"]], ")"]]]], "+", "p", "+", RowBox[List["2", " ", "c", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["c"]]]], "]"]]]], SuperscriptBox["c", RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["m", "\[Element]", "Integers"]], "&&", RowBox[List["m", ">", "0"]]]]]]]]]]

2002-12-18