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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=18/5, b>=a > For fixed z and a=18/5, b=6





http://functions.wolfram.com/07.23.03.b3aj.01









  


  








Input Form





Hypergeometric2F1[18/5, 6, 28/5, z] == (1/781250) (69 (-((25 (-526 + 298 z - 243 z^2 + 96 z^3))/(-1 + z)^4) + (1/z^(23/5)) (6 (1560 z^(3/5) + 585 z^(8/5) + 360 z^(13/5) + 260 z^(18/5) + 936 Log[1 - z^(1/5)] + 936 (-1)^(2/5) Log[1 + (-1)^(1/5) z^(1/5)] + 936 (-1)^(4/5) Log[1 - (-1)^(2/5) z^(1/5)] - 936 (-1)^(1/5) Log[1 + (-1)^(3/5) z^(1/5)] - 936 (-1)^(3/5) Log[1 - (-1)^(4/5) z^(1/5)])) + (1/z^(18/5)) (7 (520 z^(3/5) + 195 z^(8/5) + 120 z^(13/5) + 312 Log[1 - z^(1/5)] + 312 (-1)^(2/5) Log[1 + (-1)^(1/5) z^(1/5)] + 312 (-1)^(4/5) Log[1 - (-1)^(2/5) z^(1/5)] - 312 (-1)^(1/5) Log[1 + (-1)^(3/5) z^(1/5)] - 312 (-1)^(3/5) Log[1 - (-1)^(4/5) z^(1/5)]))))








Standard Form





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MathML Form







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type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 936 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 936 </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'> 2 <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'> -1 </cn> <apply> <times /> <cn type='integer'> 936 </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> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 936 </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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 195 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 8 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 520 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 312 </cn> <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> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 312 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 312 </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'> 2 <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'> -1 </cn> <apply> <times /> <cn type='integer'> 312 </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> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 312 </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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02