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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=-16/5, b>=a > For fixed z and a=-16/5, b=6





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









  


  








Input Form





Hypergeometric2F1[-(16/5), 6, -(6/5), -z] == (1/390625) (44 ((25 (22859 + 64212 z + 60822 z^2 + 19344 z^3))/(1 + z)^4 - 1624896 (-(5/11) + (5 z)/6 - 5 z^2 + z^(11/5) (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)])) + 4163796 (5 (-(1/16) + z/11 - z^2/6 + z^3) - z^(16/5) (Log[1 + z^(1/5)] - (-1)^(1/5) Log[1 - (-1)^(1/5) z^(1/5)] + (-1)^(2/5) Log[1 + (-1)^(2/5) z^(1/5)] - (-1)^(3/5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(4/5) Log[1 + (-1)^(4/5) z^(1/5)]))))








Standard Form





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MathML Form







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<cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 11 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4163796 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 6 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 11 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 16 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 16 <sep /> 5 </cn> </apply> <apply> <plus /> <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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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'> 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 /> <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'> 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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <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'> 3 <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 /> <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'> 4 <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> </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