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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=29/8, b>=a > For fixed z and a=29/8, b=31/8





http://functions.wolfram.com/07.23.03.caw6.01









  


  








Input Form





Hypergeometric2F1[29/8, 31/8, 1, z] == (1/(10465 Pi (-1 + z)^7)) (2^(3/4) (1 + Sqrt[1 - z])^(1/4) (16 (-1 + z) (1511 + 5362 z + 1575 z^2) EllipticE[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - 8 (-1 + z) (1511 + 5362 z + 1575 z^2) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1/z) (Sqrt[2] Sqrt[1 + Sqrt[1 - z]] Sqrt[1 - z] (-10465 - 76221 z - 48867 z^2 + 385 z^3) EllipticK[1/2 - 1/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]) - (1/z) (5 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (-1 + z) (2093 + 16453 z + 14063 z^2 + 1183 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> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </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