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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 4 and fixed z > For fixed z and a=-23/4, b>=a > For fixed z and a=-23/4, b=-1/2





http://functions.wolfram.com/07.23.03.9405.01









  


  








Input Form





Hypergeometric2F1[-(23/4), -(1/2), 3, z] == (8 Sqrt[2] (2 (1 - z)^(1/4) (-269192 + 5114648 z + 92178021 z^2 + 19668896 z^3 - 7686464 z^4 + 2509248 z^5 - 532272 z^6 + 53040 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-269192 + 5114648 z + 92178021 z^2 + 19668896 z^3 - 7686464 z^4 + 2509248 z^5 - 532272 z^6 + 53040 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-269192 + 5114648 z + 92178021 z^2 + 19668896 z^3 - 7686464 z^4 + 2509248 z^5 - 532272 z^6 + 53040 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-269192 + 5114648 z + 92178021 z^2 + 19668896 z^3 - 7686464 z^4 + 2509248 z^5 - 532272 z^6 + 53040 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-269192 + 5114648 z + 92178021 z^2 + 19668896 z^3 - 7686464 z^4 + 2509248 z^5 - 532272 z^6 + 53040 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (-269192 + 5249244 z - 15969865 z^2 - 114900160 z^3 + 20844000 z^4 - 8107328 z^5 + 2607216 z^6 - 542880 z^7 + 53040 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (422463195 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








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