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http://functions.wolfram.com/06.05.19.0004.01
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Abs[Gamma[1/2 + I y]] == Sqrt[Pi Sech[Pi y]] /; Element[y, Reals]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "y"]]]], "]"]], "]"]], "\[Equal]", SqrtBox[RowBox[List["\[Pi]", " ", RowBox[List["Sech", "[", RowBox[List["\[Pi]", " ", "y"]], "]"]]]]]]], "/;", RowBox[List["y", "\[Element]", "Reals"]]]]]]
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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> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation> </semantics> <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> y </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <semantics> <mo> ❘ </mo> <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation> </semantics> </mrow> <mo> ⩵ </mo> <msqrt> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> sech </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mi> y </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msqrt> </mrow> <mo> /; </mo> <mrow> <mi> y </mi> <mo> ∈ </mo> <semantics> <mi> ℝ </mi> <annotation encoding='Mathematica'> TagBox["\[DoubleStruckCapitalR]", Function[Reals]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <abs /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <pi /> <apply> <sech /> <apply> <times /> <pi /> <ci> y </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <in /> <ci> y </ci> <reals /> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["\[ImaginaryI]", " ", "y_"]]]], "]"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List["\[Pi]", " ", RowBox[List["Sech", "[", RowBox[List["\[Pi]", " ", "y"]], "]"]]]]], "/;", RowBox[List["y", "\[Element]", "Reals"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
