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http://functions.wolfram.com/01.03.22.0004.01
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FourierSinTransform[E^(-t), t, z] == Sqrt[2/Pi] (z/(z^2 + 1))
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Cell[BoxData[RowBox[List[RowBox[List["FourierSinTransform", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t"]]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], FractionBox[RowBox[List[" ", "z"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]]]]]]]
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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> <mrow> <msub> <mi> ℱ𝓈 </mi> <mi> t </mi> </msub> <mo> [ </mo> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> t </mi> </mrow> </msup> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <msqrt> <mfrac> <mn> 2 </mn> <mi> π </mi> </mfrac> </msqrt> <mo> ⁢ </mo> <mfrac> <mrow> <mtext> </mtext> <mi> z </mi> </mrow> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> ℱ𝓈 </ci> <ci> t </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> t </ci> </apply> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["FourierSinTransform", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "t_"]]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], " ", "z"]], RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
