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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=13/4





http://functions.wolfram.com/07.23.03.ac2t.01









  


  








Input Form





Hypergeometric2F1[-(7/2), 13/4, 4, z] == (1/(135135 Pi Sqrt[1 + Sqrt[1 - z]] z^3)) (2 Sqrt[2] (-2 (1 - z)^(1/4) (3584 + 4256 z + 11984 z^2 - 223352 z^3 + 466576 z^4 - 365750 z^5 + 100947 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (3584 + 4256 z + 11984 z^2 - 223352 z^3 + 466576 z^4 - 365750 z^5 + 100947 z^6) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (3584 + 2464 z + 9520 z^2 - 94776 z^3 + 175640 z^4 - 128326 z^5 + 33649 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (3584 + 4256 z + 11984 z^2 - 223352 z^3 + 466576 z^4 - 365750 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (3584 + 4256 z + 11984 z^2 - 223352 z^3 + 466576 z^4 - 365750 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (3584 + 4256 z + 11984 z^2 - 223352 z^3 + 466576 z^4 - 365750 z^5 + 100947 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 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