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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=15/4





http://functions.wolfram.com/07.23.03.a9pl.01









  


  








Input Form





Hypergeometric2F1[-(19/4), 15/4, 5, -z] == (1/(985747455 Pi z^4)) (4096 (1 + z)^(1/4) (8 (1824 + 988 z - 1995 z^2 + 7980 z^3 + 86541 z^4 + 194670 z^5 + 197316 z^6 + 96720 z^7 + 18720 z^8) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 4 (1824 + 988 z - 1995 z^2 + 7980 z^3 + 86541 z^4 + 194670 z^5 + 197316 z^6 + 96720 z^7 + 18720 z^8) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + Sqrt[1 + z] (-7296 + 1520 z + 5985 z^2 - 35910 z^3 + 162561 z^4 + 779688 z^5 + 1093680 z^6 + 661440 z^7 + 149760 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