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variants of this functions
Hypergeometric2F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For integer and half-integer parameters and fixed z > For fixed z and a=11/2, b>=a > For fixed z and a=11/2, b=11/2





http://functions.wolfram.com/07.23.03.4483.01









  


  










Input Form





Hypergeometric2F1[11/2, 11/2, 2, z] == -((1/(2835 Pi (-1 + z)^9 z)) (4 ((35 + z (4052 + z (16434 + z (11156 + 1091 z)))) EllipticE[z] + (-1 + z) (35 + z (2652 + z (8730 + z (4652 + 315 z)))) EllipticK[z])))










Standard Form





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MathML Form







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</mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 315 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 4652 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 8730 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 2652 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mn> 35 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> K </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Hypergeometric2F1 </ci> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='rational'> 11 <sep /> 2 </cn> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2835 </cn> <pi /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 9 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 1091 </cn> <ci> z </ci> </apply> <cn type='integer'> 11156 </cn> </apply> </apply> <cn type='integer'> 16434 </cn> </apply> </apply> <cn type='integer'> 4052 </cn> </apply> </apply> <cn type='integer'> 35 </cn> </apply> <apply> <times /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 315 </cn> <ci> z </ci> </apply> <cn type='integer'> 4652 </cn> </apply> </apply> <cn type='integer'> 8730 </cn> </apply> </apply> <cn type='integer'> 2652 </cn> </apply> </apply> <cn type='integer'> 35 </cn> </apply> <apply> <times /> <ci> K </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02