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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Specific values > For rational parameters with denominators 4 and fixed z > For fixed z and a=23/4, b>=a > For fixed z and a=23/4, b=23/4





http://functions.wolfram.com/07.23.03.anr8.01









  


  








Input Form





Hypergeometric2F1[23/4, 23/4, 6, -z] == (16384 Sqrt[2] (-(((2048 + 10400 z + 21459 z^2 + 23130 z^3 + 15063 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5) - ((2048 + 10400 z + 21459 z^2 + 23130 z^3 + 15063 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^(9/2) + ((2048 + 10400 z + 21459 z^2 + 23130 z^3 + 15063 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])/(1 + z)^5 + (1/(1 + z)^(11/2)) ((2048 + 11936 z + 29115 z^2 + 38559 z^3 + 31197 z^4 + 21945 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])])))/ (96316605 Pi z^5 Sqrt[1 + Sqrt[1 + z]])








Standard Form





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MathML Form







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<cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 11 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </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