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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=-1/4





http://functions.wolfram.com/07.23.03.a8gf.01









  


  








Input Form





Hypergeometric2F1[-(21/4), -(1/4), 4, z] == (1/(555179625 Pi z^3)) (256 (2 (3808 - 50813 z + 413287 z^2 + 8856278 z^3 + 1116950 z^4 - 378937 z^5 + 112547 z^6 - 22048 z^7 + 2048 z^8) EllipticE[(1/2) (1 - Sqrt[1 - z])] + Sqrt[1 - z] (-3808 + 49861 z - 401268 z^2 - 4613690 z^3 - 77500 z^4 + 24477 z^5 - 5144 z^6 + 512 z^7) EllipticK[(1/2) (1 - Sqrt[1 - z])] - (3808 - 50813 z + 413287 z^2 + 8856278 z^3 + 1116950 z^4 - 378937 z^5 + 112547 z^6 - 22048 z^7 + 2048 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