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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=3/4





http://functions.wolfram.com/07.23.03.a9er.01









  


  










Input Form





Hypergeometric2F1[-(19/4), 3/4, 5, -z] == (1/(27460107675 Pi z^4)) (4096 (1 + z)^(1/4) (2 (-80256 - 745712 z - 3182025 z^2 - 8778000 z^3 + 3678090 z^4 + 2316132 z^5 + 985959 z^6 + 248820 z^7 + 28080 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] + 2 Sqrt[1 + z] (40128 + 342760 z + 1338645 z^2 + 3423420 z^3 + 2440230 z^4 + 1718964 z^5 + 817245 z^6 + 227760 z^7 + 28080 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] - (-80256 - 745712 z - 3182025 z^2 - 8778000 z^3 + 3678090 z^4 + 2316132 z^5 + 985959 z^6 + 248820 z^7 + 28080 z^8) EllipticK[1/2 - 1/(2 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