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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=-21/8, b>=a > For fixed z and a=-21/8, b=6





http://functions.wolfram.com/07.23.03.bm8b.01









  


  








Input Form





Hypergeometric2F1[-(21/8), 6, -(5/8), z] == (1/83886080) (91 (-((256 (-106715 + 296747 z - 279045 z^2 + 88245 z^3))/ (-1 + z)^4) - 53741205 ((-(8/65)) (5 + 13 z) + z^(13/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) + 156105405 (-(8/21) - (8 z)/13 - (8 z^2)/5 + z^(21/8) (-Log[1 - z^(1/8)] - I Log[1 - I z^(1/8)] + I Log[1 + I z^(1/8)] + Log[1 + z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)]))))








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 8 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> 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Date Added to functions.wolfram.com (modification date)





2007-05-02