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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=-47/8, b>=a > For fixed z and a=-47/8, b=45/8





http://functions.wolfram.com/07.23.03.b5s4.01









  


  










Input Form





Hypergeometric2F1[-(47/8), 45/8, 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (1098088448 + 2226202752 z + 5834767765 z^2 + 21584602655 z^3 + 146140298115 z^4 - 2994277225639 z^5 + 10713014456144 z^6 - 17397455074560 z^7 + 14869380218880 z^8 - 6541904117760 z^9 + 1173561016320 z^10) 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) (1098088448 + 2226202752 z + 5834767765 z^2 + 21584602655 z^3 + 146140298115 z^4 - 2994277225639 z^5 + 10713014456144 z^6 - 17397455074560 z^7 + 14869380218880 z^8 - 6541904117760 z^9 + 1173561016320 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (1098088448 + 2226202752 z + 5834767765 z^2 + 21584602655 z^3 + 146140298115 z^4 - 2994277225639 z^5 + 10713014456144 z^6 - 17397455074560 z^7 + 14869380218880 z^8 - 6541904117760 z^9 + 1173561016320 z^10) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (1098088448 + 1814419584 z + 4887344773 z^2 + 19108474865 z^3 + 137287362135 z^4 + 3983461945211 z^5 - 27478659871432 z^6 + 71091793118016 z^7 - 95553499176960 z^8 + 71516999516160 z^9 - 28416941752320 z^10 + 4694244065280 z^11) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (1844230409956079145 Pi (1 + Sqrt[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