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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 8 and fixed z and a<0 > For fixed z and a=-23/8, b>=a > For fixed z and a=-23/8, b=-11/8





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









  


  










Input Form





Hypergeometric2F1[-(23/8), -(11/8), 4, z] == (2048 2^(1/4) (2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (32384 - 405559 z + 3294060 z^2 + 38690374 z^3 + 19853068 z^4 + 62073 z^5) EllipticE[1/2 - (1 - z)^(1/4)/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (32384 - 405559 z + 3294060 z^2 + 38690374 z^3 + 19853068 z^4 + 62073 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - Sqrt[1 - z] (32384 - 405559 z + 3294060 z^2 + 38690374 z^3 + 19853068 z^4 + 62073 z^5) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] - (32384 - 417703 z + 3442824 z^2 - 46530146 z^3 - 71448596 z^4 - 8379855 z^5 + 248292 z^6) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (86041670715 Pi (1 + Sqrt[1 - z])^(1/4) z^3)










Standard Form





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MathML Form







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<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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 248292 </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'> 8379855 </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'> 71448596 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn 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Rule Form





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





2007-05-02