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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=-7/2, b>=a > For fixed z and a=-7/2, b=-1/4





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









  


  








Input Form





Hypergeometric2F1[-(7/2), -(1/4), 6, z] == (32 Sqrt[2] (2 (32768 - 361472 z + 1898304 z^2 - 6615200 z^3 + 20400800 z^4 + 122941824 z^5 + 2882724 z^6 - 388518 z^7 + 29835 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (32768 - 361472 z + 1898304 z^2 - 6615200 z^3 + 20400800 z^4 + 122941824 z^5 + 2882724 z^6 - 388518 z^7 + 29835 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (32768 - 361472 z + 1898304 z^2 - 6615200 z^3 + 20400800 z^4 + 122941824 z^5 + 2882724 z^6 - 388518 z^7 + 29835 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (32768 - 361472 z + 1898304 z^2 - 6615200 z^3 + 20400800 z^4 + 122941824 z^5 + 2882724 z^6 - 388518 z^7 + 29835 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (32768 - 361472 z + 1898304 z^2 - 6615200 z^3 + 20400800 z^4 + 122941824 z^5 + 2882724 z^6 - 388518 z^7 + 29835 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (-32768 + 345088 z - 1730880 z^2 + 5801120 z^3 - 17745280 z^4 - 35833824 z^5 + 2591004 z^6 - 364650 z^7 + 29835 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (1523106585 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








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