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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=-21/4, b>=a > For fixed z and a=-21/4, b=-13/4





http://functions.wolfram.com/07.23.03.a89i.01









  


  








Input Form





Hypergeometric2F1[-(21/4), -(13/4), 4, z] == (1/(2775898125 Pi z^3)) (256 (-2 (-1248 + 32097 z - 610350 z^2 - 52609925 z^3 - 185091800 z^4 - 148503833 z^5 - 26529078 z^6 - 168675 z^7 + 3900 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] - Sqrt[1 - z] (1248 - 31785 z + 602550 z^2 + 31070225 z^3 + 96354100 z^4 + 68373993 z^5 + 10368150 z^6 + 975 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] + (-1248 + 32097 z - 610350 z^2 - 52609925 z^3 - 185091800 z^4 - 148503833 z^5 - 26529078 z^6 - 168675 z^7 + 3900 z^8) EllipticK[(1/2) (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