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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=9/4





http://functions.wolfram.com/07.23.03.a81a.01









  


  










Input Form





Hypergeometric2F1[-(11/2), 9/4, 3, z] == (-2 (1 - z)^(1/4) (59136 + 133056 z - 3122432 z^2 + 10193760 z^3 - 15411600 z^4 + 12465596 z^5 - 5249244 z^6 + 908523 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (59136 + 133056 z - 3122432 z^2 + 10193760 z^3 - 15411600 z^4 + 12465596 z^5 - 5249244 z^6 + 908523 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (59136 + 103488 z - 1392704 z^2 + 4082080 z^3 - 5784720 z^4 + 4460516 z^5 - 1807432 z^6 + 302841 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (59136 + 133056 z - 3122432 z^2 + 10193760 z^3 - 15411600 z^4 + 12465596 z^5 - 5249244 z^6 + 908523 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (59136 + 133056 z - 3122432 z^2 + 10193760 z^3 - 15411600 z^4 + 12465596 z^5 - 5249244 z^6 + 908523 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (59136 + 133056 z - 3122432 z^2 + 10193760 z^3 - 15411600 z^4 + 12465596 z^5 - 5249244 z^6 + 908523 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (450450 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