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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=-19/4





http://functions.wolfram.com/07.23.03.a869.01









  


  










Input Form





Hypergeometric2F1[-(21/4), -(19/4), 3, -z] == (1/(145568097675 Pi z^2)) (64 (1 + z)^(1/4) (-2 (1293292 + 63047985 z - 8226663318 z^2 + 52727147895 z^3 - 84034916280 z^4 + 39224536239 z^5 - 4640248830 z^6 + 63293769 z^7) EllipticE[1/2 - 1/(2 Sqrt[1 + z])] - 4 Sqrt[1 + z] (-323323 - 15519504 z + 931016805 z^2 - 4357378920 z^3 + 4941663615 z^4 - 1480865736 z^5 + 85038807 z^6) EllipticK[1/2 - 1/(2 Sqrt[1 + z])] + (1293292 + 63047985 z - 8226663318 z^2 + 52727147895 z^3 - 84034916280 z^4 + 39224536239 z^5 - 4640248830 z^6 + 63293769 z^7) EllipticK[1/2 - 1/(2 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