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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=3/8





http://functions.wolfram.com/07.23.03.bf1i.01









  


  








Input Form





Hypergeometric2F1[-(31/8), 3/8, 1, z] == (2 2^(1/4) (-8 Sqrt[1 - z] (-5339 + 7178 z - 4689 z^2 + 1170 z^3) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - 4 Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (-5339 + 7178 z - 4689 z^2 + 1170 z^3) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + 4 Sqrt[1 - z] (-5339 + 7178 z - 4689 z^2 + 1170 z^3) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (53509 - 70238 z + 76909 z^2 - 42660 z^3 + 9360 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (74865 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]])








Standard Form





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MathML Form







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</apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02