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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 4 and fixed z > For fixed z and a=3/4, b>=a > For fixed z and a=3/4, b=19/4





http://functions.wolfram.com/07.23.03.aj7e.01









  


  








Input Form





Hypergeometric2F1[3/4, 19/4, 5, -z] == (4096 Sqrt[2] (16 (-8 + 7 z - 7 z^2 + 8 z^3) (1 + z + Sqrt[1 + z]) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + (128 (1 + Sqrt[1 + z]) - 32 z^3 (1 + 4 Sqrt[1 + z]) - 16 z (1 + 7 Sqrt[1 + z]) + z^2 (19 + 112 Sqrt[1 + z])) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (225225 Pi z^4 Sqrt[1 + z] Sqrt[1 + Sqrt[1 + z]])








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