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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=-11/4, b>=a > For fixed z and a=-11/4, b=-3/4





http://functions.wolfram.com/07.23.03.ad3l.01









  


  








Input Form





Hypergeometric2F1[-(11/4), -(3/4), 5, -z] == (4096 Sqrt[2] (-4 Sqrt[1 + z] (32 + 324 z + 1665 z^2 + 7126 z^3 - 23832 z^4 + 1710 z^5 + 95 z^6) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] - 4 (32 + 356 z + 1989 z^2 + 8791 z^3 - 16706 z^4 - 22122 z^5 + 1805 z^6 + 95 z^7) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (128 + 1392 z + 7623 z^2 + 33412 z^3 + 136338 z^4 - 140220 z^5 + 95 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + 4 Sqrt[1 + z] (32 + 324 z + 1665 z^2 + 7126 z^3 - 23832 z^4 + 1710 z^5 + 95 z^6) EllipticK[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])]))/(431548425 Pi z^4 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