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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=-21/4, b>=a > For fixed z and a=-21/4, b=9/2





http://functions.wolfram.com/07.23.03.a8un.01









  


  










Input Form





Hypergeometric2F1[-(21/4), 9/2, 2, z] == (-2 (15912 - 2897576 z + 28026710 z^2 - 94319895 z^3 + 144282105 z^4 - 103268781 z^5 + 28164213 z^6) EllipticE[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - 2 Sqrt[1 - z] (15912 - 2897576 z + 28026710 z^2 - 94319895 z^3 + 144282105 z^4 - 103268781 z^5 + 28164213 z^6) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(3/4) (15912 - 1497320 z + 11008030 z^2 - 26960715 z^3 + 26823060 z^4 - 9388071 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (15912 - 2897576 z + 28026710 z^2 - 94319895 z^3 + 144282105 z^4 - 103268781 z^5 + 28164213 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + (1 - z)^(1/4) (15912 - 2897576 z + 28026710 z^2 - 94319895 z^3 + 144282105 z^4 - 103268781 z^5 + 28164213 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + Sqrt[1 - z] (15912 - 2897576 z + 28026710 z^2 - 94319895 z^3 + 144282105 z^4 - 103268781 z^5 + 28164213 z^6) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])])/ (348075 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] 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