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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=-31/8, b>=a > For fixed z and a=-31/8, b=-11/8





http://functions.wolfram.com/07.23.03.bew3.01









  


  










Input Form





Hypergeometric2F1[-(31/8), -(11/8), 5, z] == (65536 2^(1/4) (-4 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (365056 - 5030928 z + 37118067 z^2 - 244309450 z^3 - 2738632470 z^4 - 1593324096 z^5 - 9625077 z^6 + 485298 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (365056 - 5030928 z + 37118067 z^2 - 244309450 z^3 - 2738632470 z^4 - 1593324096 z^5 - 9625077 z^6 + 485298 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + 2 Sqrt[1 - z] (365056 - 5030928 z + 37118067 z^2 - 244309450 z^3 - 2738632470 z^4 - 1593324096 z^5 - 9625077 z^6 + 485298 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (730112 - 10335648 z + 77934465 z^2 - 515465489 z^3 + 6554289210 z^4 + 10620943998 z^5 + 1558696293 z^6 - 78860925 z^7 + 3882384 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (388478143278225 Pi (1 + Sqrt[1 - z])^(1/4) z^4)










Standard Form





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MathML Form







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<apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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> <power /> <apply> <times /> <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> <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> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 3882384 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 78860925 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1558696293 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 10620943998 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6554289210 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 515465489 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 77934465 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 10335648 </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