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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=-9/2





http://functions.wolfram.com/07.23.03.9053.01









  


  










Input Form





Hypergeometric2F1[-(23/4), -(9/2), 3, z] == (2 (1 - z)^(1/4) (-391552 + 19577600 z + 1835816688 z^2 + 10816850224 z^3 + 15844940632 z^4 + 6590402952 z^5 + 621700023 z^6 + 1118208 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + 2 (1 - z)^(3/4) (-391552 + 19577600 z + 1835816688 z^2 + 10816850224 z^3 + 15844940632 z^4 + 6590402952 z^5 + 621700023 z^6 + 1118208 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(1/4) (-391552 + 19577600 z + 1835816688 z^2 + 10816850224 z^3 + 15844940632 z^4 + 6590402952 z^5 + 621700023 z^6 + 1118208 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - Sqrt[1 - z] (-391552 + 19577600 z + 1835816688 z^2 + 10816850224 z^3 + 15844940632 z^4 + 6590402952 z^5 + 621700023 z^6 + 1118208 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - (1 - z)^(3/4) (-391552 + 19577600 z + 1835816688 z^2 + 10816850224 z^3 + 15844940632 z^4 + 6590402952 z^5 + 621700023 z^6 + 1118208 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (391552 - 19773376 z - 361525520 z^2 + 2551457312 z^3 + 14344759384 z^4 + 14980043852 z^5 + 4036738755 z^6 + 199041024 z^7 - 1118208 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)])/ (366134769 Sqrt[2] Pi Sqrt[1 + Sqrt[1 - z]] z^2)










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2007-05-02