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http://functions.wolfram.com/01.24.26.0025.01
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Sech[Pi z] == (Gamma[1/2 - I z] Gamma[1/2 + I z])/Pi
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Cell[BoxData[RowBox[List[RowBox[List["Sech", "[", RowBox[List["\[Pi]", " ", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "\[Pi]"]]]]]
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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> <mi> sech </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <mi> Γ </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> Γ </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> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <sech /> <apply> <times /> <pi /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </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> Gamma </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Sech", "[", RowBox[List["\[Pi]", " ", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]], "\[Pi]"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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