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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Specialized values > For fixed a, b, z





http://functions.wolfram.com/07.23.03.0104.01









  


  










Input Form





Hypergeometric2F1[a, b, 2 b, z] == 2^(2 b - 1) Gamma[b + 1/2] z^(1/2 - b) (1 - z)^((2 b - 2 a - 1)/4) LegendreP[a - b - 1/2, 1/2 - b, 3, (2 - z)/(2 Sqrt[1 - z])] /; Re[(2 - z)/(2 Sqrt[1 - z])] > 0










Standard Form





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MathML Form







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</mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <ci> a </ci> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> &#120083; 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Rule Form





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





2001-10-29