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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 5 and fixed z > For fixed z and a=12/5, b>=a > For fixed z and a=12/5, b=5





http://functions.wolfram.com/07.23.03.b1rh.01









  


  










Input Form





Hypergeometric2F1[12/5, 5, 22/5, -z] == (1/15625) (17 (-((25 (-31 + 3 z + 9 z^2))/(1 + z)^3) + (1/z^(12/5)) (12 (-35 z^(2/5) + 10 z^(7/5) - 14 Log[1 + z^(1/5)] + 14 (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] + 14 (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] - 14 (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] - 14 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)])) + (1/z^(17/5)) (3 (210 z^(2/5) - 60 z^(7/5) + 35 z^(12/5) + 84 Log[1 + z^(1/5)] - 84 (-1)^(3/5) Log[1 - (-1)^(1/5) z^(1/5)] - 84 (-1)^(1/5) Log[1 + (-1)^(2/5) z^(1/5)] + 84 (-1)^(4/5) Log[1 - (-1)^(3/5) z^(1/5)] + 84 (-1)^(2/5) Log[1 + (-1)^(4/5) z^(1/5)]))))










Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <ln /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </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 /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </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'> 3 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 84 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> 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Rule Form





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





2007-05-02