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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=-17/4, b>=a > For fixed z and a=-17/4, b=-1/2





http://functions.wolfram.com/07.23.03.aag0.01









  


  










Input Form





Hypergeometric2F1[-(17/4), -(1/2), 3, z] == (8 Sqrt[2] (-2 (5304 - 82212 z - 2061765 z^2 - 726400 z^3 + 171200 z^4 - 35392 z^5 + 3696 z^6) EllipticE[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (5304 - 82212 z - 2061765 z^2 - 726400 z^3 + 171200 z^4 - 35392 z^5 + 3696 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (-5304 + 79560 z + 795435 z^2 + 48400 z^3 - 10800 z^4 + 1232 z^5) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (5304 - 82212 z - 2061765 z^2 - 726400 z^3 + 171200 z^4 - 35392 z^5 + 3696 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (5304 - 82212 z - 2061765 z^2 - 726400 z^3 + 171200 z^4 - 35392 z^5 + 3696 z^6) EllipticK[1/2 - (1 - z)^(1/4)/ (1 + Sqrt[1 - z])] + Sqrt[1 - z] (5304 - 82212 z - 2061765 z^2 - 726400 z^3 + 171200 z^4 - 35392 z^5 + 3696 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (5221125 Pi Sqrt[1 + Sqrt[1 - z]] z^2)










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