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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=-9/2, b>=a > For fixed z and a=-9/2, b=-11/4





http://functions.wolfram.com/07.23.03.a9z6.01









  


  








Input Form





Hypergeometric2F1[-(9/2), -(11/4), 3, z] == (2 (1 - z)^(1/4) (-2688 + 81984 z + 3747440 z^2 + 9542880 z^3 + 4250040 z^4 + 169708 z^5 - 4389 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-2688 + 81984 z + 3747440 z^2 + 9542880 z^3 + 4250040 z^4 + 169708 z^5 - 4389 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (2688 - 83328 z - 283280 z^2 + 6032080 z^3 + 9776040 z^4 + 2339312 z^5 + 1463 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (2688 - 81984 z - 3747440 z^2 - 9542880 z^3 - 4250040 z^4 - 169708 z^5 + 4389 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (2688 - 81984 z - 3747440 z^2 - 9542880 z^3 - 4250040 z^4 - 169708 z^5 + 4389 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (2688 - 81984 z - 3747440 z^2 - 9542880 z^3 - 4250040 z^4 - 169708 z^5 + 4389 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/(855855 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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