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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=9/4





http://functions.wolfram.com/07.23.03.a81b.01









  


  








Input Form





Hypergeometric2F1[-(11/2), 9/4, 4, z] == (-2 (1 - z)^(1/4) (-473088 + 1330560 z + 1862784 z^2 - 24929216 z^3 + 60761760 z^4 - 73581768 z^5 + 49691840 z^6 - 17968566 z^7 + 2725569 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-473088 + 1330560 z + 1862784 z^2 - 24929216 z^3 + 60761760 z^4 - 73581768 z^5 + 49691840 z^6 - 17968566 z^7 + 2725569 z^8) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-473088 + 1567104 z + 1241856 z^2 - 10647872 z^3 + 23707360 z^4 - 27182088 z^5 + 17620904 z^6 - 6162574 z^7 + 908523 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-473088 + 1330560 z + 1862784 z^2 - 24929216 z^3 + 60761760 z^4 - 73581768 z^5 + 49691840 z^6 - 17968566 z^7 + 2725569 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-473088 + 1330560 z + 1862784 z^2 - 24929216 z^3 + 60761760 z^4 - 73581768 z^5 + 49691840 z^6 - 17968566 z^7 + 2725569 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-473088 + 1330560 z + 1862784 z^2 - 24929216 z^3 + 60761760 z^4 - 73581768 z^5 + 49691840 z^6 - 17968566 z^7 + 2725569 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (3828825 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