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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=-25/8, b>=a > For fixed z and a=-25/8, b=-19/8





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









  


  








Input Form





Hypergeometric2F1[-(25/8), -(19/8), 1, z] == (1/(799425 Pi)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (4 (1348477 + 7997929 z + 4715191 z^2 + 131043 z^3) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (3 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (266475 + 1929931 z + 1308073 z^2 + 43681 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - 2 (1348477 + 7997929 z + 4715191 z^2 + 131043 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (159885 + 1267769 z + 1226471 z^2 + 184403 z^3) EllipticK[ 1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])])))








Standard Form





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MathML Form







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</apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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