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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 8 and fixed z and a<0 > For fixed z and a=-31/8, b>=a > For fixed z and a=-31/8, b=27/8





http://functions.wolfram.com/07.23.03.bfg5.01









  


  










Input Form





Hypergeometric2F1[-(31/8), 27/8, 2, z] == (16 2^(1/4) (-2 Sqrt[1 - z] (274505 - 16049669 z + 68098056 z^2 - 89478480 z^3 + 37128000 z^4) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (274505 - 16049669 z + 68098056 z^2 - 89478480 z^3 + 37128000 z^4) EllipticE[ 2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[1 - z] (274505 - 16049669 z + 68098056 z^2 - 89478480 z^3 + 37128000 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (274505 + 9204791 z - 89353264 z^2 + 225526080 z^3 - 219797760 z^4 + 74256000 z^5) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (203408205 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z)










Standard Form





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MathML Form







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<power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02