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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=-9/2, b>=a > For fixed z and a=-9/2, b=1/4





http://functions.wolfram.com/07.23.03.aa1f.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 1/4, 3, z] == (2 (1 - z)^(1/4) (-1920 + 21120 z + 101168 z^2 - 58800 z^3 + 28776 z^4 - 8624 z^5 + 1155 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + 2 (1 - z)^(3/4) (-1920 + 21120 z + 101168 z^2 - 58800 z^3 + 28776 z^4 - 8624 z^5 + 1155 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (1920 - 21120 z - 101168 z^2 + 58800 z^3 - 28776 z^4 + 8624 z^5 - 1155 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + Sqrt[1 - z] (1920 - 21120 z - 101168 z^2 + 58800 z^3 - 28776 z^4 + 8624 z^5 - 1155 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (1920 - 21120 z - 101168 z^2 + 58800 z^3 - 28776 z^4 + 8624 z^5 - 1155 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1920 - 22080 z + 89392 z^2 + 21184 z^3 - 10104 z^4 + 2948 z^5 - 385 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)])/(45045 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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