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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=15/4





http://functions.wolfram.com/07.23.03.aa4p.01









  


  








Input Form





Hypergeometric2F1[-(9/2), 15/4, 4, z] == (1/(495495 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (Sqrt[2] (2 (-3072 - 9024 z - 50400 z^2 + 986624 z^3 - 2933792 z^4 + 3673020 z^5 - 2141490 z^6 + 480675 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (-3072 - 9024 z - 50400 z^2 + 986624 z^3 - 2933792 z^4 + 3673020 z^5 - 2141490 z^6 + 480675 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (3072 + 9024 z + 50400 z^2 - 986624 z^3 + 2933792 z^4 - 3673020 z^5 + 2141490 z^6 - 480675 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (3072 + 9024 z + 50400 z^2 - 986624 z^3 + 2933792 z^4 - 3673020 z^5 + 2141490 z^6 - 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (3072 + 9024 z + 50400 z^2 - 986624 z^3 + 2933792 z^4 - 3673020 z^5 + 2141490 z^6 - 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (3072 + 10560 z + 56160 z^2 + 34336 z^3 - 1096160 z^4 + 2267460 z^5 - 1756950 z^6 + 480675 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - 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