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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=23/4





http://functions.wolfram.com/07.23.03.a84p.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 23/4, 4, z] == (-2 (43008 + 508032 z + 7133952 z^2 - 338720960 z^3 + 1956098400 z^4 - 4649404120 z^5 + 5475080520 z^6 - 3179953530 z^7 + 729183975 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (43008 + 508032 z + 7133952 z^2 - 338720960 z^3 + 1956098400 z^4 - 4649404120 z^5 + 5475080520 z^6 - 3179953530 z^7 + 729183975 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (43008 + 529536 z + 7405440 z^2 - 43941440 z^3 - 328943200 z^4 + 1895269480 z^5 - 3397795440 z^6 + 2596606350 z^7 - 729183975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (43008 + 508032 z + 7133952 z^2 - 338720960 z^3 + 1956098400 z^4 - 4649404120 z^5 + 5475080520 z^6 - 3179953530 z^7 + 729183975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (43008 + 508032 z + 7133952 z^2 - 338720960 z^3 + 1956098400 z^4 - 4649404120 z^5 + 5475080520 z^6 - 3179953530 z^7 + 729183975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (43008 + 508032 z + 7133952 z^2 - 338720960 z^3 + 1956098400 z^4 - 4649404120 z^5 + 5475080520 z^6 - 3179953530 z^7 + 729183975 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (72747675 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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