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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=3/2





http://functions.wolfram.com/07.23.03.9623.01









  


  








Input Form





Hypergeometric2F1[-(23/4), 3/2, 3, z] == (32 Sqrt[2] (-2 (1 - z)^(1/4) (-336490 + 1177715 z - 7117881 z^2 + 14850415 z^3 - 16805567 z^4 + 10946793 z^5 - 3875235 z^6 + 580125 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (-336490 + 1177715 z - 7117881 z^2 + 14850415 z^3 - 16805567 z^4 + 10946793 z^5 - 3875235 z^6 + 580125 z^7) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (-336490 + 1177715 z - 7117881 z^2 + 14850415 z^3 - 16805567 z^4 + 10946793 z^5 - 3875235 z^6 + 580125 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (-336490 + 1177715 z - 7117881 z^2 + 14850415 z^3 - 16805567 z^4 + 10946793 z^5 - 3875235 z^6 + 580125 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (-336490 + 1177715 z - 7117881 z^2 + 14850415 z^3 - 16805567 z^4 + 10946793 z^5 - 3875235 z^6 + 580125 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (-336490 + 1345960 z + 1126124 z^2 - 8089232 z^3 + 16736462 z^4 - 18420584 z^5 + 11629020 z^6 - 3991260 z^7 + 580125 z^8) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (140821065 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1345960 </cn> <ci> z </ci> </apply> <cn type='integer'> -336490 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 140821065 </cn> <pi /> <apply> <power /> 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Rule Form





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





2007-05-02