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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=-13/5, b>=a > For fixed z and a=-13/5, b=3





http://functions.wolfram.com/07.23.03.atd6.01









  


  








Input Form





Hypergeometric2F1[-(13/5), 3, 7/5, z] == (1/(15625 z^(2/5))) (12505 z^(2/5) - 47385 z^(7/5) + 35880 z^(12/5) + 312 (-4 + 52 z - 117 z^2 + 69 z^3) Log[1 - z^(1/5)] - 312 (-1)^(3/5) (-4 + 52 z - 117 z^2 + 69 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 1248 (-1)^(1/5) Log[1 - (-1)^(2/5) z^(1/5)] - 16224 (-1)^(1/5) z Log[1 - (-1)^(2/5) z^(1/5)] + 36504 (-1)^(1/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] - 21528 (-1)^(1/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 1248 (-1)^(4/5) Log[1 + (-1)^(3/5) z^(1/5)] + 16224 (-1)^(4/5) z Log[1 + (-1)^(3/5) z^(1/5)] - 36504 (-1)^(4/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] + 21528 (-1)^(4/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] - 1248 (-1)^(2/5) Log[1 - (-1)^(4/5) z^(1/5)] + 16224 (-1)^(2/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 36504 (-1)^(2/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 21528 (-1)^(2/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)])








Standard Form





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MathML Form







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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'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <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> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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'> 4 <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'> 35880 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 12 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 36504 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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'> 2 </cn> </apply> </apply> <apply> 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type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 47385 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 16224 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 16224 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <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> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 16224 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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'> 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> <times /> <cn type='integer'> 12505 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> 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Rule Form





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





2007-05-02