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http://functions.wolfram.com/01.06.21.0186.01
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Integrate[E^z^2 Sin[z], z] == (1/4) E^(1/4) Sqrt[Pi]
(Erf[1/2 - I z] + Erf[1/2 + I z])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z", "2"]], " ", RowBox[List["Sin", "[", "z", "]"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["1", "/", "4"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", RowBox[List[FractionBox["1", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["Erf", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "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> <msup> <mi> ⅇ </mi> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </msup> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> ⁢ </mo> <mroot> <mi> ⅇ </mi> <mn> 4 </mn> </mroot> <mo> ⁢ </mo> <msqrt> <mi> π </mi> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> - </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <sin /> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <power /> <exponentiale /> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Erf </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> Erf </ci> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", SuperscriptBox["z_", "2"]], " ", RowBox[List["Sin", "[", "z_", "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["1", "/", "4"]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List["Erf", "[", RowBox[List[FractionBox["1", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["Erf", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], ")"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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