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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=-37/8, b>=a > For fixed z and a=-37/8, b=39/8





http://functions.wolfram.com/07.23.03.bc7y.01









  


  










Input Form





Hypergeometric2F1[-(37/8), 39/8, 6, z] == (524288 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (457080832 - 101771904 z - 167346153 z^2 - 420353115 z^3 - 1996311135 z^4 + 26237148707 z^5 - 64466940384 z^6 + 69469500672 z^7 - 35679621120 z^8 + 7169310720 z^9) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[1 - z] (457080832 - 101771904 z - 167346153 z^2 - 420353115 z^3 - 1996311135 z^4 + 26237148707 z^5 - 64466940384 z^6 + 69469500672 z^7 - 35679621120 z^8 + 7169310720 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (457080832 - 101771904 z - 167346153 z^2 - 420353115 z^3 - 1996311135 z^4 + 26237148707 z^5 - 64466940384 z^6 + 69469500672 z^7 - 35679621120 z^8 + 7169310720 z^9) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] - (457080832 - 273177216 z - 176050329 z^2 - 372061677 z^3 - 1832270895 z^4 - 41397228103 z^5 + 205509612924 z^6 - 377347981824 z^7 + 343214496768 z^8 - 156459663360 z^9 + 28677242880 z^10) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (17937727563921165 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^5)










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