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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=1/8, b>=a > For fixed z and a=1/8, b=27/8





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









  


  










Input Form





Hypergeometric2F1[1/8, 27/8, 5, z] == -((65536 2^(1/4) ((2 + Sqrt[2 - 2 Sqrt[1 - z]]) Sqrt[1 - z] (-3072 + 800 z + 745 z^2 + 900 z^3) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - (-3072 (1 + Sqrt[1 - z]) + 160 (17 + 5 Sqrt[1 - z]) z + (560 + 745 Sqrt[1 - z]) z^2 + 100 (5 + 9 Sqrt[1 - z]) z^3 + 1800 z^4) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (78233925 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] 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