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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=9/8, b>=a > For fixed z and a=9/8, b=21/8





http://functions.wolfram.com/07.23.03.c2bn.01









  


  








Input Form





Hypergeometric2F1[9/8, 21/8, 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (3072 - 3040 z + 33 z^2) EllipticE[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (3072 (1 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) - 32 (131 + 95 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + 95 Sqrt[1 - z]) z + 33 (26 + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) + Sqrt[1 - z]) z^2 + 132 z^3) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1726725 Pi (1 + Sqrt[1 - z])^(1/4) z^4)








Standard Form





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MathML Form







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Rule Form





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





2007-05-02