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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=-23/4, b>=a > For fixed z and a=-23/4, b=7/2





http://functions.wolfram.com/07.23.03.9874.01









  


  










Input Form





Hypergeometric2F1[-(23/4), 7/2, 1, z] == (2 (1 - z)^(1/4) (1208572 - 16298272 z + 63524937 z^2 - 105234675 z^3 + 79003743 z^4 - 22207185 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (1208572 - 16298272 z + 63524937 z^2 - 105234675 z^3 + 79003743 z^4 - 22207185 z^5) EllipticE[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-1208572 + 16298272 z - 63524937 z^2 + 105234675 z^3 - 79003743 z^4 + 22207185 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-1208572 + 16298272 z - 63524937 z^2 + 105234675 z^3 - 79003743 z^4 + 22207185 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-1208572 + 16298272 z - 63524937 z^2 + 105234675 z^3 - 79003743 z^4 + 22207185 z^5) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-400996 + 549144 z + 17285209 z^2 - 73680516 z^3 + 117482274 z^4 - 83445180 z^5 + 22207185 z^6) EllipticK[ (2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (201894 Sqrt[2] Pi 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