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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=-11/4





http://functions.wolfram.com/07.23.03.a7xi.01









  


  








Input Form





Hypergeometric2F1[-(11/2), -(11/4), 2, z] == (2 (1 - z)^(1/4) (14784 + 1816288 z + 8621920 z^2 + 6828480 z^3 + 534380 z^4 - 32494 z^5 + 1617 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (14784 + 1816288 z + 8621920 z^2 + 6828480 z^3 + 534380 z^4 - 32494 z^5 + 1617 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-14784 - 367456 z + 3008320 z^2 + 10536320 z^3 + 4612180 z^4 + 10934 z^5 - 539 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(1/4) (14784 + 1816288 z + 8621920 z^2 + 6828480 z^3 + 534380 z^4 - 32494 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (14784 + 1816288 z + 8621920 z^2 + 6828480 z^3 + 534380 z^4 - 32494 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(3/4) (14784 + 1816288 z + 8621920 z^2 + 6828480 z^3 + 534380 z^4 - 32494 z^5 + 1617 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (360360 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z)








Standard Form





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MathML Form







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</math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02