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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=-7/2, b>=a > For fixed z and a=-7/2, b=-5/4





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









  


  








Input Form





Hypergeometric2F1[-(7/2), -(5/4), 4, z] == (2 Sqrt[2] (-2 (-17920 + 245280 z - 2182320 z^2 - 47442008 z^3 - 34813896 z^4 - 298350 z^5 + 16575 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (-17920 + 245280 z - 2182320 z^2 - 47442008 z^3 - 34813896 z^4 - 298350 z^5 + 16575 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (-17920 + 245280 z - 2182320 z^2 - 47442008 z^3 - 34813896 z^4 - 298350 z^5 + 16575 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (-17920 + 245280 z - 2182320 z^2 - 47442008 z^3 - 34813896 z^4 - 298350 z^5 + 16575 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (-17920 + 245280 z - 2182320 z^2 - 47442008 z^3 - 34813896 z^4 - 298350 z^5 + 16575 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (17920 - 236320 z + 2066960 z^2 + 18575128 z^3 + 8009040 z^4 - 285090 z^5 + 16575 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (29864835 Pi Sqrt[1 + Sqrt[1 - z]] z^3)








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