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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=-7/4, b>=a > For fixed z and a=-7/4, b=21/4





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









  


  








Input Form





Hypergeometric2F1[-(7/4), 21/4, 5, -z] == (4096 Sqrt[2] (Sqrt[1 + z] (-2688 + 7952 z - 21987 z^2 + 83328 z^3 + 1095680 z^4 + 983040 z^5) EllipticE[(-1 + Sqrt[1 + z])/ (1 + Sqrt[1 + z])] + (-2688 + 5264 z - 14035 z^2 + 61341 z^3 + 1179008 z^4 + 2078720 z^5 + 983040 z^6) EllipticE[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - 2 (-1344 + 2968 z - 7917 z^2 + 33096 z^3 + 171520 z^4 + 122880 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])] - Sqrt[1 + z] (-2688 + 7952 z - 21987 z^2 + 83328 z^3 + 1095680 z^4 + 983040 z^5) EllipticK[(-1 + Sqrt[1 + z])/(1 + Sqrt[1 + z])]))/ (1673196525 Pi z^4 Sqrt[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