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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=-19/4, b>=a > For fixed z and a=-19/4, b=-19/4





http://functions.wolfram.com/07.23.03.a905.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(19/4), 1, -z] == (1/(7315 Pi Sqrt[1 + Sqrt[1 + z]])) (2 Sqrt[2] (2 Sqrt[1 + z] (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] + 2 (5021 - 60799 z + 75378 z^2 + 75378 z^3 - 60799 z^4 + 5021 z^5) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 Sqrt[1 + z] (5021 - 65820 z + 141198 z^2 - 65820 z^3 + 5021 z^4) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - (2727 + 40479 z - 386810 z^2 + 537566 z^3 - 162077 z^4 + 7315 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + 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