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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=-11/2, b>=a > For fixed z and a=-11/2, b=1/4





http://functions.wolfram.com/07.23.03.a7zl.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 1/4, 2, z] == (2 (1 - z)^(1/4) (73920 + 1021024 z - 1046720 z^2 + 890688 z^3 - 494692 z^4 + 157850 z^5 - 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (73920 + 1021024 z - 1046720 z^2 + 890688 z^3 - 494692 z^4 + 157850 z^5 - 21945 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-73920 + 457376 z + 392992 z^2 - 323872 z^3 + 174244 z^4 - 54010 z^5 + 7315 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-73920 - 1021024 z + 1046720 z^2 - 890688 z^3 + 494692 z^4 - 157850 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-73920 - 1021024 z + 1046720 z^2 - 890688 z^3 + 494692 z^4 - 157850 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-73920 - 1021024 z + 1046720 z^2 - 890688 z^3 + 494692 z^4 - 157850 z^5 + 21945 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (360360 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] 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