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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=-3/2, b>=a > For fixed z and a=-3/2, b=13/4





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









  


  








Input Form





Hypergeometric2F1[-(3/2), 13/4, 6, z] == (1/(945945 Pi Sqrt[1 + Sqrt[1 - z]] z^5)) (128 Sqrt[2] (-2 (1 - z)^(1/4) (8192 - 20224 z + 9296 z^2 + 4816 z^3 + 5236 z^4 - 18326 z^5 + 8085 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (8192 - 20224 z + 9296 z^2 + 4816 z^3 + 5236 z^4 - 18326 z^5 + 8085 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (8192 - 24320 z + 18640 z^2 + 1680 z^3 + 2660 z^4 - 6622 z^5 + 2695 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] + (1 - z)^(1/4) (8192 - 20224 z + 9296 z^2 + 4816 z^3 + 5236 z^4 - 18326 z^5 + 8085 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (8192 - 20224 z + 9296 z^2 + 4816 z^3 + 5236 z^4 - 18326 z^5 + 8085 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (8192 - 20224 z + 9296 z^2 + 4816 z^3 + 5236 z^4 - 18326 z^5 + 8085 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