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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=-11/4, b>=a > For fixed z and a=-11/4, b=1/2





http://functions.wolfram.com/07.23.03.ad6v.01









  


  








Input Form





Hypergeometric2F1[-(11/4), 1/2, 5, z] == (256 Sqrt[2] (2 (1 - z)^(1/4) (-1408 + 10560 z - 36036 z^2 + 82159 z^3 + 35760 z^4 - 9360 z^5 + 1200 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-1408 + 10560 z - 36036 z^2 + 82159 z^3 + 35760 z^4 - 9360 z^5 + 1200 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(1/4) (-1408 + 10560 z - 36036 z^2 + 82159 z^3 + 35760 z^4 - 9360 z^5 + 1200 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-1408 + 10560 z - 36036 z^2 + 82159 z^3 + 35760 z^4 - 9360 z^5 + 1200 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)] - (1 - z)^(3/4) (-1408 + 10560 z - 36036 z^2 + 82159 z^3 + 35760 z^4 - 9360 z^5 + 1200 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-1408 + 11264 z - 41184 z^2 + 99253 z^3 - 179840 z^4 + 37440 z^5 - 9600 z^6 + 1200 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/ (2 z)]))/(22713075 Pi Sqrt[1 + Sqrt[1 - z]] z^4)








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