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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=-5/2





http://functions.wolfram.com/07.23.03.a95s.01









  


  








Input Form





Hypergeometric2F1[-(19/4), -(5/2), 3, z] == (2 Sqrt[2] (-2 (1 - z)^(1/4) (6688 - 200640 z - 8889552 z^2 - 21496252 z^3 - 8454261 z^4 - 96768 z^5 + 3840 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] - 2 (1 - z)^(3/4) (6688 - 200640 z - 8889552 z^2 - 21496252 z^3 - 8454261 z^4 - 96768 z^5 + 3840 z^6) EllipticE[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(1/4) (6688 - 200640 z - 8889552 z^2 - 21496252 z^3 - 8454261 z^4 - 96768 z^5 + 3840 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + Sqrt[1 - z] (6688 - 200640 z - 8889552 z^2 - 21496252 z^3 - 8454261 z^4 - 96768 z^5 + 3840 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (1 - z)^(3/4) (6688 - 200640 z - 8889552 z^2 - 21496252 z^3 - 8454261 z^4 - 96768 z^5 + 3840 z^6) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)] + (6688 - 203984 z - 613152 z^2 + 14311064 z^3 + 21496793 z^4 + 4223232 z^5 - 97536 z^6 + 3840 z^7) EllipticK[(2 (-1 + Sqrt[1 - z]) (1 - z)^(1/4) + z)/(2 z)]))/ (8176707 Pi Sqrt[1 + Sqrt[1 - z]] z^2)








Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> 3840 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 96768 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8454261 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21496252 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 8889552 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 200640 </cn> <ci> z </ci> </apply> </apply> <cn 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Rule Form





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





2007-05-02