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http://functions.wolfram.com/06.32.21.0010.01
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Integrate[Cos[b z] FresnelS[a Sqrt[z]], z] ==
-((1/(32 b^3 - 8 a^4 b Pi^2))
((1 - I) (a Sqrt[Pi] (Sqrt[2 b - a^2 Pi] (2 b + a^2 Pi)
Erf[(1/2 + I/2) Sqrt[2 b - a^2 Pi] Sqrt[z]] +
(-2 b + a^2 Pi) Sqrt[2 b + a^2 Pi] Erf[(1/2 + I/2) Sqrt[2 b + a^2 Pi]
Sqrt[z]] + 2 b Sqrt[2 b - a^2 Pi]
Erfi[(1/2 + I/2) Sqrt[2 b - a^2 Pi] Sqrt[z]] +
a^2 Pi Sqrt[2 b - a^2 Pi] Erfi[(1/2 + I/2) Sqrt[2 b - a^2 Pi]
Sqrt[z]] - 2 b Sqrt[2 b + a^2 Pi]
Erfi[(1/2 + I/2) Sqrt[2 b + a^2 Pi] Sqrt[z]] +
a^2 Pi Sqrt[2 b + a^2 Pi] Erfi[(1/2 + I/2) Sqrt[2 b + a^2 Pi]
Sqrt[z]]) - (4 + 4 I) (4 b^2 - a^4 Pi^2) FresnelS[a Sqrt[z]]
Sin[b z])))
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["FresnelS", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["-", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["32", " ", SuperscriptBox["b", "3"]]], "-", RowBox[List["8", " ", SuperscriptBox["a", "4"], " ", "b", " ", SuperscriptBox["\[Pi]", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]], ")"]], " ", RowBox[List["Erf", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["Erf", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List["2", " ", "b", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", RowBox[List["Erfi", "[", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "+", FractionBox["\[ImaginaryI]", "2"]]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "\[Pi]"]]]]], " ", SqrtBox["z"]]], "]"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["4", "+", RowBox[List["4", " ", "\[ImaginaryI]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["\[Pi]", "2"]]]]], ")"]], " ", RowBox[List["FresnelS", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox["S", FresnelS] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mn> 32 </mn> <mo> ⁢ </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <mi> π </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mi> erfi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> ⅈ </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msqrt> <mrow> <mrow> <mi> π </mi> <mo> ⁢ </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mi> ⅈ </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> a </mi> <mn> 4 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> π </mi> <mn> 2 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <semantics> <mi> S </mi> <annotation encoding='Mathematica'> TagBox["S", FresnelS] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> FresnelS </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <ci> b </ci> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> 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b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <pi /> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <pi /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='complex-cartesian'> 4 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <pi /> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <ci> FresnelS </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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