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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.abuh.01









  


  








Input Form





Hypergeometric2F1[-(15/4), 11/2, 4, z] == (8 Sqrt[2] (-2 (1 - z)^(1/4) (1408 + 12408 z + 124344 z^2 - 3594310 z^3 + 12010245 z^4 - 13843440 z^5 + 5287425 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (1408 + 12408 z + 124344 z^2 - 3594310 z^3 + 12010245 z^4 - 13843440 z^5 + 5287425 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (1408 + 12408 z + 124344 z^2 - 3594310 z^3 + 12010245 z^4 - 13843440 z^5 + 5287425 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (1408 + 12408 z + 124344 z^2 - 3594310 z^3 + 12010245 z^4 - 13843440 z^5 + 5287425 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (1408 + 12408 z + 124344 z^2 - 3594310 z^3 + 12010245 z^4 - 13843440 z^5 + 5287425 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1408 + 11704 z + 118008 z^2 - 250750 z^3 - 4197895 z^4 + 13932945 z^5 - 14900925 z^6 + 5287425 z^7) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (13627845 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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