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http://functions.wolfram.com/01.08.07.0002.01
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Tan[z] == (2/Pi) Integrate[(t^((2 z)/Pi) - 1)/(t^2 - 1), {t, 0, Infinity}] /;
0 < Re[z] < Pi/2
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Tan", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["2", " "]], "\[Pi]"], RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["t", FractionBox[RowBox[List["2", " ", "z"]], "\[Pi]"]], "-", "1"]], RowBox[List[SuperscriptBox["t", "2"], "-", "1"]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]
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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> <mi> tan </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mn> 2 </mn> <mtext> </mtext> </mrow> <mi> π </mi> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mi> ∞ </mi> </msubsup> <mrow> <mfrac> <mrow> <msup> <mi> t </mi> <mfrac> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mi> π </mi> </mfrac> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mrow> <msup> <mi> t </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> t </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 0 </mn> <mo> < </mo> <mrow> <mi> Re </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> < </mo> <mfrac> <mi> π </mi> <mn> 2 </mn> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <tan /> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <int /> <bvar> <ci> t </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> t </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> t </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <lt /> <cn type='integer'> 0 </cn> <apply> <real /> <ci> z </ci> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <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["Tan", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["t", FractionBox[RowBox[List["2", " ", "z"]], "\[Pi]"]], "-", "1"]], RowBox[List[SuperscriptBox["t", "2"], "-", "1"]]], RowBox[List["\[DifferentialD]", "t"]]]]]]]], "\[Pi]"], "/;", RowBox[List["0", "<", RowBox[List["Re", "[", "z", "]"]], "<", FractionBox["\[Pi]", "2"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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