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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=-5/2, b>=a > For fixed z and a=-5/2, b=17/4





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









  


  








Input Form





Hypergeometric2F1[-(5/2), 17/4, 5, z] == (32 Sqrt[2] (2 (1 - z)^(1/4) (-3072 - 2816 z - 4240 z^2 - 11712 z^3 + 174284 z^4 - 251636 z^5 + 100947 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-3072 - 2816 z - 4240 z^2 - 11712 z^3 + 174284 z^4 - 251636 z^5 + 100947 z^6) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-3072 - 1280 z - 2544 z^2 - 9184 z^3 + 70964 z^4 - 90288 z^5 + 33649 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-3072 - 2816 z - 4240 z^2 - 11712 z^3 + 174284 z^4 - 251636 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-3072 - 2816 z - 4240 z^2 - 11712 z^3 + 174284 z^4 - 251636 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-3072 - 2816 z - 4240 z^2 - 11712 z^3 + 174284 z^4 - 251636 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (1756755 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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