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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=7/8, b>=a > For fixed z and a=7/8, b=5





http://functions.wolfram.com/07.23.03.c1cv.01









  


  








Input Form





Hypergeometric2F1[7/8, 5, 31/8, z] == (1/33554432) (805 (-((1024 (-35 + 27 z))/(-1 + z)^2) - (1/z^(23/8)) (9 (120 z^(7/8) + 56 z^(15/8) + 105 Log[1 - z^(1/8)] + 105 I Log[1 - I z^(1/8)] - 105 I Log[1 + I z^(1/8)] - 105 Log[1 + z^(1/8)] + 105 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 105 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 105 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 105 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(15/8)) (306 (8 z^(7/8) + 7 Log[1 - z^(1/8)] + 7 I Log[1 - I z^(1/8)] - 7 I Log[1 + I z^(1/8)] - 7 Log[1 + z^(1/8)] + 7 (-1)^(1/4) Log[1 - (-1)^(1/4) z^(1/8)] - 7 (-1)^(1/4) Log[1 + (-1)^(1/4) z^(1/8)] + 7 (-1)^(3/4) Log[1 - (-1)^(3/4) z^(1/8)] - 7 (-1)^(3/4) Log[1 + (-1)^(3/4) z^(1/8)])) - (1/z^(7/8)) (3825 (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='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 105 </cn> <imaginaryi /> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <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 /> <cn type='integer'> 105 </cn> <imaginaryi /> <apply> <ln /> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 105 </cn> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> 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Rule Form





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





2007-05-02