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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=-37/8, b>=a > For fixed z and a=-37/8, b=-1/8





http://functions.wolfram.com/07.23.03.bbk7.01









  


  










Input Form





Hypergeometric2F1[-(37/8), -(1/8), 4, z] == (2048 2^(1/4) (-2 Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-12498304 + 147929145 z - 1036968660 z^2 - 20539401170 z^3 - 252740700 z^4 + 78670305 z^5 - 16819800 z^6 + 1713600 z^7) EllipticE[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[1 - z] (-12498304 + 147929145 z - 1036968660 z^2 - 20539401170 z^3 - 252740700 z^4 + 78670305 z^5 - 16819800 z^6 + 1713600 z^7) EllipticK[1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z] (-12498304 + 147929145 z - 1036968660 z^2 - 20539401170 z^3 - 252740700 z^4 + 78670305 z^5 - 16819800 z^6 + 1713600 z^7) EllipticK[ 1/2 - Sqrt[1 - z]/(Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])] + (-12498304 + 152616009 z - 1091160525 z^2 - 2477399030 z^3 + 4300914150 z^4 - 1154953395 z^5 + 346190295 z^6 - 70563600 z^7 + 6854400 z^8) EllipticK[1/2 - Sqrt[1 - z]/ (Sqrt[2] Sqrt[1 + Sqrt[1 - z] - z])]))/ (18112129615125 Pi (1 + Sqrt[1 - z])^(1/4) (1 - z)^(1/4) z^3)










Standard Form





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MathML Form







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<cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 346190295 </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'> 1154953395 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4300914150 </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'> 2477399030 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1091160525 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 152616009 </cn> <ci> z </ci> </apply> <cn type='integer'> -12498304 </cn> 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Rule Form





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





2007-05-02