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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=-39/8, b>=a > For fixed z and a=-39/8, b=21/8





http://functions.wolfram.com/07.23.03.bad6.01









  


  










Input Form





Hypergeometric2F1[-(39/8), 21/8, 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (91264 - 104811 z - 314433 z^2 + 2534675 z^3 - 5041575 z^4 + 4723488 z^5 - 2188032 z^6 + 405504 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (91264 - 104811 z - 314433 z^2 + 2534675 z^3 - 5041575 z^4 + 4723488 z^5 - 2188032 z^6 + 405504 z^7) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (91264 - 104811 z - 314433 z^2 + 2534675 z^3 - 5041575 z^4 + 4723488 z^5 - 2188032 z^6 + 405504 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (91264 - 139035 z - 284487 z^2 - 4712257 z^3 + 18198675 z^4 - 28374192 z^5 + 22915200 z^6 - 9529344 z^7 + 1622016 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (7547514975 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










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