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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=-23/4, b>=a > For fixed z and a=-23/4, b=1/2





http://functions.wolfram.com/07.23.03.9496.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 1/2, 1, z] == (1/(168245 Pi Sqrt[1 + Sqrt[1 - z]])) (2 Sqrt[2] (-26 (1 - z)^(1/4) (-9446 + 23615 z - 32628 z^2 + 25327 z^3 - 10438 z^4 + 1785 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 26 (1 - z)^(3/4) (-9446 + 23615 z - 32628 z^2 + 25327 z^3 - 10438 z^4 + 1785 z^5) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 13 (1 - z)^(1/4) (-9446 + 23615 z - 32628 z^2 + 25327 z^3 - 10438 z^4 + 1785 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 13 Sqrt[1 - z] (-9446 + 23615 z - 32628 z^2 + 25327 z^3 - 10438 z^4 + 1785 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 13 (1 - z)^(3/4) (-9446 + 23615 z - 32628 z^2 + 25327 z^3 - 10438 z^4 + 1785 z^5) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (45447 - 136341 z + 348683 z^2 - 470131 z^3 + 352677 z^4 - 140335 z^5 + 23205 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))








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