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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=-29/8, b>=a > For fixed z and a=-29/8, b=-23/8





http://functions.wolfram.com/07.23.03.bg9j.01









  


  










Input Form





Hypergeometric2F1[-(29/8), -(23/8), 4, z] == (2048 2^(1/4) (2 Sqrt[1 - z] (597632 - 11303649 z + 153353305 z^2 + 3000382822 z^3 + 4222872834 z^4 + 1000489931 z^5 + 16185813 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + Sqrt[2 - 2 Sqrt[1 - z]] Sqrt[1 - z] (597632 - 11303649 z + 153353305 z^2 + 3000382822 z^3 + 4222872834 z^4 + 1000489931 z^5 + 16185813 z^6) EllipticE[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] - Sqrt[1 - z] (597632 - 11303649 z + 153353305 z^2 + 3000382822 z^3 + 4222872834 z^4 + 1000489931 z^5 + 16185813 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])] + (-597632 + 11677169 z - 160356805 z^2 + 4715419818 z^3 + 17166831286 z^4 + 10674458869 z^5 + 1122882047 z^6) EllipticK[2 - (2 Sqrt[2])/(Sqrt[2] + Sqrt[1 - Sqrt[1 - z]])]))/ (7803993256605 Pi Sqrt[Sqrt[2] + Sqrt[1 - Sqrt[1 - z]]] z^3)










Standard Form





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MathML Form







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type='integer'> 160356805 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 11677169 </cn> <ci> z </ci> </apply> <cn type='integer'> -597632 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </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 /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> 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Rule Form





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





2007-05-02