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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=-13/4, b>=a > For fixed z and a=-13/4, b=-5/2





http://functions.wolfram.com/07.23.03.ac7z.01









  


  










Input Form





Hypergeometric2F1[-(13/4), -(5/2), 6, z] == (64 Sqrt[2] (2 (16384 - 251392 z + 1959840 z^2 - 11169680 z^3 + 66038600 z^4 + 1277352048 z^5 + 1272619546 z^6 + 216878585 z^7 + 2365440 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (16384 - 251392 z + 1959840 z^2 - 11169680 z^3 + 66038600 z^4 + 1277352048 z^5 + 1272619546 z^6 + 216878585 z^7 + 2365440 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (16384 - 243200 z + 1840800 z^2 - 10286000 z^3 + 61165000 z^4 + 504919608 z^5 + 348300370 z^6 + 36223495 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (16384 - 251392 z + 1959840 z^2 - 11169680 z^3 + 66038600 z^4 + 1277352048 z^5 + 1272619546 z^6 + 216878585 z^7 + 2365440 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (16384 - 251392 z + 1959840 z^2 - 11169680 z^3 + 66038600 z^4 + 1277352048 z^5 + 1272619546 z^6 + 216878585 z^7 + 2365440 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (16384 - 251392 z + 1959840 z^2 - 11169680 z^3 + 66038600 z^4 + 1277352048 z^5 + 1272619546 z^6 + 216878585 z^7 + 2365440 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (25649298675 Pi Sqrt[1 + Sqrt[1 - z]] z^5)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02