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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=-19/8, b>=a > For fixed z and a=-19/8, b=-7/8





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









  


  










Input Form





Hypergeometric2F1[-(19/8), -(7/8), 6, z] == (524288 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticE[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + (-6848512 + 74504320 z - 387627075 z^2 + 1350868365 z^3 - 4251944070 z^4 + 28450376322 z^5 + 15362847145 z^6 + 15247505 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z]] (1 - z)^(1/4) (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticK[ 1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])] + Sqrt[1 - z] (-6848512 + 71936128 z - 361353267 z^2 + 1222364088 z^3 - 3826935882 z^4 - 15344461380 z^5 - 2119403195 z^6 + 60990020 z^7) EllipticK[1/2 - (1 - z)^(1/4)/(Sqrt[2] Sqrt[1 + Sqrt[1 - z]])]))/ (11132673648801705 Pi (1 + Sqrt[1 - z])^(1/4) z^5)










Standard Form





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MathML Form







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<apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 15344461380 </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'> 3826935882 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 1222364088 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 361353267 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 71936128 </cn> <ci> z </ci> </apply> <cn type='integer'> -6848512 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times 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</math>










Rule Form





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





2007-05-02