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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=-2/5, b>=a > For fixed z and a=-2/5, b=4





http://functions.wolfram.com/07.23.03.ax1t.01









  


  








Input Form





Hypergeometric2F1[-(2/5), 4, 13/5, z] == (1/(15625 (-1 + z) z^(8/5))) (8 (35 z^(3/5) - 1695 z^(8/5) + 1785 z^(13/5) + 21 (1 + 7 z - 42 z^2 + 34 z^3) Log[1 - z^(1/5)] + 21 (-1)^(2/5) (1 + 7 z - 42 z^2 + 34 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 21 (-1)^(4/5) Log[1 - (-1)^(2/5) z^(1/5)] + 147 (-1)^(4/5) z Log[1 - (-1)^(2/5) z^(1/5)] - 882 (-1)^(4/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 714 (-1)^(4/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 21 (-1)^(1/5) Log[1 + (-1)^(3/5) z^(1/5)] - 147 (-1)^(1/5) z Log[1 + (-1)^(3/5) z^(1/5)] + 882 (-1)^(1/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 714 (-1)^(1/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 21 (-1)^(3/5) Log[1 - (-1)^(4/5) z^(1/5)] - 147 (-1)^(3/5) z Log[1 - (-1)^(4/5) z^(1/5)] + 882 (-1)^(3/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] - 714 (-1)^(3/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)]))








Standard Form





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MathML Form







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<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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 714 </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'> 3 <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> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> 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<cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 34 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 42 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <ci> z </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> 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Rule Form





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





2007-05-02