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http://functions.wolfram.com/06.37.22.0002.01
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MellinTransform[SinIntegral[t], t, z] == (-(Gamma[z]/z)) Sin[(Pi z)/2] /;
-1 < Re[z] < 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MellinTransform", "[", RowBox[List[RowBox[List["SinIntegral", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["Gamma", "[", "z", "]"]], "z"]]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], "2"], "]"]]]]]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]
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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> <mrow> <msub> <mi> ℳ </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <mi> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ] </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mi> z </mi> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mi> sin </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> < </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> < </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <apply> <ci> Subscript </ci> <ci> ℳ </ci> <ci> t </ci> </apply> <apply> <ci> SinIntegral </ci> <ci> t </ci> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Gamma </ci> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <cn type='integer'> -1 </cn> <apply> <real /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MellinTransform", "[", RowBox[List[RowBox[List["SinIntegral", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["Gamma", "[", "z", "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["\[Pi]", " ", "z"]], "2"], "]"]]]], "z"]]], "/;", RowBox[List[RowBox[List["-", "1"]], "<", RowBox[List["Re", "[", "z", "]"]], "<", "0"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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