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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 8 and fixed z and a<0 > For fixed z and a=-41/8, b>=a > For fixed z and a=-41/8, b=-21/8





http://functions.wolfram.com/07.23.03.b8sb.01









  


  










Input Form





Hypergeometric2F1[-(41/8), -(21/8), 5, z] == (65536 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-117765120 + 2363889440 z - 26933212625 z^2 + 295798610250 z^3 + 17596079499005 z^4 + 39785429290924 z^5 + 18802807288377 z^6 + 1296616043450 z^7 - 38683715525 z^8 + 1242018960 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - 4 (-29441280 + 602012840 z - 6951898910 z^2 + 76415647275 z^3 + 1065516427370 z^4 + 478043942611 z^5 - 1191114870258 z^6 - 420127158703 z^7 - 2432287130 z^8 + 77626185 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (-117765120 + 2363889440 z - 26933212625 z^2 + 295798610250 z^3 + 17596079499005 z^4 + 39785429290924 z^5 + 18802807288377 z^6 + 1296616043450 z^7 - 38683715525 z^8 + 1242018960 z^9) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-117765120 + 2363889440 z - 26933212625 z^2 + 295798610250 z^3 + 17596079499005 z^4 + 39785429290924 z^5 + 18802807288377 z^6 + 1296616043450 z^7 - 38683715525 z^8 + 1242018960 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (433380604160629125 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^4)










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