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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=17/4





http://functions.wolfram.com/07.23.03.a834.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 17/4, 3, z] == (-2 (1 - z)^(1/4) (19712 + 340032 z - 27305856 z^2 + 170284384 z^3 - 416604336 z^4 + 495447876 z^5 - 287900844 z^6 + 65716497 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (19712 + 340032 z - 27305856 z^2 + 170284384 z^3 - 416604336 z^4 + 495447876 z^5 - 287900844 z^6 + 65716497 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (19712 + 330176 z - 13423680 z^2 + 72643360 z^3 - 162738800 z^4 + 181405692 z^5 - 100139424 z^6 + 21905499 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (19712 + 340032 z - 27305856 z^2 + 170284384 z^3 - 416604336 z^4 + 495447876 z^5 - 287900844 z^6 + 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (19712 + 340032 z - 27305856 z^2 + 170284384 z^3 - 416604336 z^4 + 495447876 z^5 - 287900844 z^6 + 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (19712 + 340032 z - 27305856 z^2 + 170284384 z^3 - 416604336 z^4 + 495447876 z^5 - 287900844 z^6 + 65716497 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (3513510 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02