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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=-11/2, b>=a > For fixed z and a=-11/2, b=19/4





http://functions.wolfram.com/07.23.03.a83o.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 19/4, 4, z] == (-2 (6144 + 46464 z + 477312 z^2 - 17007680 z^3 + 80754400 z^4 - 163388360 z^5 + 167659440 z^6 - 86329230 z^7 + 17784975 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (6144 + 46464 z + 477312 z^2 - 17007680 z^3 + 80754400 z^4 - 163388360 z^5 + 167659440 z^6 - 86329230 z^7 + 17784975 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (6144 + 49536 z + 503040 z^2 - 1432640 z^3 - 17992800 z^4 + 74530040 z^5 - 109978440 z^6 + 72101250 z^7 - 17784975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (6144 + 46464 z + 477312 z^2 - 17007680 z^3 + 80754400 z^4 - 163388360 z^5 + 167659440 z^6 - 86329230 z^7 + 17784975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (6144 + 46464 z + 477312 z^2 - 17007680 z^3 + 80754400 z^4 - 163388360 z^5 + 167659440 z^6 - 86329230 z^7 + 17784975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (6144 + 46464 z + 477312 z^2 - 17007680 z^3 + 80754400 z^4 - 163388360 z^5 + 167659440 z^6 - 86329230 z^7 + 17784975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (3828825 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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