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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=-15/4, b>=a > For fixed z and a=-15/4, b=11/2





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









  


  








Input Form





Hypergeometric2F1[-(15/4), 11/2, 6, z] == (512 Sqrt[2] (-2 (1 - z)^(1/4) (22528 + 33088 z + 62524 z^2 + 162470 z^3 + 745745 z^4 - 10748080 z^5 + 23065770 z^6 - 18650190 z^7 + 5287425 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (22528 + 33088 z + 62524 z^2 + 162470 z^3 + 745745 z^4 - 10748080 z^5 + 23065770 z^6 - 18650190 z^7 + 5287425 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (22528 + 33088 z + 62524 z^2 + 162470 z^3 + 745745 z^4 - 10748080 z^5 + 23065770 z^6 - 18650190 z^7 + 5287425 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (22528 + 33088 z + 62524 z^2 + 162470 z^3 + 745745 z^4 - 10748080 z^5 + 23065770 z^6 - 18650190 z^7 + 5287425 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (22528 + 33088 z + 62524 z^2 + 162470 z^3 + 745745 z^4 - 10748080 z^5 + 23065770 z^6 - 18650190 z^7 + 5287425 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (22528 + 21824 z + 43868 z^2 + 127050 z^3 + 656425 z^4 + 411145 z^5 - 12793690 z^6 + 25949820 z^7 - 19707675 z^8 + 5287425 z^9) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (2957242365 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








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