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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > Values at z=1/2 > For fixed a, b





http://functions.wolfram.com/07.23.03.0023.01









  


  








Input Form





Hypergeometric2F1[a, b, (a + b - 1)/2, 1/2] == ((2^(b - 1) Gamma[(a + b - 1)/2])/Gamma[b]) (Gamma[1 + b/2]/Gamma[(1 + a)/2] + Gamma[b/2]/Gamma[(a - 1)/2] + (2 Gamma[(1 + b)/2])/Gamma[a/2])








Standard Form





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MathML Form







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</mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mfrac> <mo> + </mo> <mfrac> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mi> b </mi> <mn> 2 </mn> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <times /> <ci> b </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29