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variants of this functions
Hypergeometric2F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1Regularized[a,b,c,z] > Specific values > Specialized values > For fixed z and integer parameters





http://functions.wolfram.com/07.24.03.0222.01









  


  








Input Form





Hypergeometric2F1Regularized[1, 2, m + 3/2, z] == 1/((1 - z) Gamma[1/2 + m]) - ((2 (-1 + z)^(-2 + m))/ (z^m Gamma[-(1/2) + m])) ((Sqrt[1 - z]/Sqrt[z]) ArcSin[Sqrt[z]] - Sum[(1/(2 k - 1)) (z/(z - 1))^(Sign[m] k - UnitStep[m]), {k, 1, Abs[m]}]) /; Element[m, Integers]








Standard Form





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MathML Form







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</mo> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mi> z </mi> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> m </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </munderover> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> z </mi> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> ) </mo> </mrow> <mrow> <mrow> <mrow> <mi> sgn </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> m </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mrow> <semantics> <mi> &#952; 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02