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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=-7/2, b>=a > For fixed z and a=-7/2, b=-13/4





http://functions.wolfram.com/07.23.03.abx6.01









  


  








Input Form





Hypergeometric2F1[-(7/2), -(13/4), 6, z] == (32 Sqrt[2] (2 (32768 - 570368 z + 5136192 z^2 - 34631200 z^3 + 250336000 z^4 + 6474312096 z^5 + 9302429444 z^6 + 2831258914 z^7 + 144987645 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] + 2 Sqrt[1 - z] (32768 - 570368 z + 5136192 z^2 - 34631200 z^3 + 250336000 z^4 + 6474312096 z^5 + 9302429444 z^6 + 2831258914 z^7 + 144987645 z^8) EllipticE[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(3/4) (32768 - 553984 z + 4864320 z^2 - 32283040 z^3 + 234912800 z^4 + 2693882016 z^5 + 2816264132 z^6 + 591449210 z^7 + 15862275 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (32768 - 570368 z + 5136192 z^2 - 34631200 z^3 + 250336000 z^4 + 6474312096 z^5 + 9302429444 z^6 + 2831258914 z^7 + 144987645 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - (1 - z)^(1/4) (32768 - 570368 z + 5136192 z^2 - 34631200 z^3 + 250336000 z^4 + 6474312096 z^5 + 9302429444 z^6 + 2831258914 z^7 + 144987645 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])] - Sqrt[1 - z] (32768 - 570368 z + 5136192 z^2 - 34631200 z^3 + 250336000 z^4 + 6474312096 z^5 + 9302429444 z^6 + 2831258914 z^7 + 144987645 z^8) EllipticK[1/2 - (1 - z)^(1/4)/(1 + Sqrt[1 - z])]))/ (62291153925 Pi Sqrt[1 + Sqrt[1 - z]] z^5)








Standard Form





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MathML Form







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type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2693882016 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 234912800 </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'> 32283040 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4864320 </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'> 553984 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 32768 </cn> </apply> <apply> <ci> EllipticK </ci> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 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Rule Form





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





2007-05-02