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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=-3/8





http://functions.wolfram.com/07.23.03.ba08.01









  


  










Input Form





Hypergeometric2F1[-(39/8), -(3/8), 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (14237184 - 179596144 z + 1166920755 z^2 - 6298841640 z^3 - 43278594590 z^4 - 1877245524 z^5 + 439211619 z^6 - 74901420 z^7 + 6320160 z^8) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (14237184 - 179596144 z + 1166920755 z^2 - 6298841640 z^3 - 43278594590 z^4 - 1877245524 z^5 + 439211619 z^6 - 74901420 z^7 + 6320160 z^8) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[1 - z] (14237184 - 179596144 z + 1166920755 z^2 - 6298841640 z^3 - 43278594590 z^4 - 1877245524 z^5 + 439211619 z^6 - 74901420 z^7 + 6320160 z^8) EllipticK[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (28474368 - 369870176 z + 2465618883 z^2 - 13437593715 z^3 + 133273551950 z^4 + 91787762682 z^5 - 16640546769 z^6 + 3795438537 z^7 - 623438640 z^8 + 50561280 z^9) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (7055847206983575 Pi (1 + Sqrt[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