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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=-19/4, b>=a > For fixed z and a=-19/4, b=-1/2





http://functions.wolfram.com/07.23.03.a9aw.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(1/2), 3, z] == (8 Sqrt[2] (-2 (1 - z)^(1/4) (11704 - 193116 z - 2835585 z^2 - 456064 z^3 + 134592 z^4 - 29376 z^5 + 3120 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (11704 - 193116 z - 2835585 z^2 - 456064 z^3 + 134592 z^4 - 29376 z^5 + 3120 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (11704 - 193116 z - 2835585 z^2 - 456064 z^3 + 134592 z^4 - 29376 z^5 + 3120 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (11704 - 193116 z - 2835585 z^2 - 456064 z^3 + 134592 z^4 - 29376 z^5 + 3120 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (11704 - 193116 z - 2835585 z^2 - 456064 z^3 + 134592 z^4 - 29376 z^5 + 3120 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (11704 - 198968 z + 666837 z^2 + 3250592 z^3 - 478528 z^4 + 139968 z^5 - 30000 z^6 + 3120 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (13627845 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