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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=9/4





http://functions.wolfram.com/07.23.03.aa37.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 9/4, 3, z] == (2 (1 - z)^(1/4) (-8064 - 16128 z + 302768 z^2 - 787344 z^3 + 891000 z^4 - 479864 z^5 + 100947 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-8064 - 16128 z + 302768 z^2 - 787344 z^3 + 891000 z^4 - 479864 z^5 + 100947 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (8064 + 16128 z - 302768 z^2 + 787344 z^3 - 891000 z^4 + 479864 z^5 - 100947 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (8064 + 16128 z - 302768 z^2 + 787344 z^3 - 891000 z^4 + 479864 z^5 - 100947 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (8064 + 16128 z - 302768 z^2 + 787344 z^3 - 891000 z^4 + 479864 z^5 - 100947 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (8064 + 12096 z - 131408 z^2 + 306208 z^3 - 324360 z^4 + 166364 z^5 - 33649 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/(45045 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