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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=-11/5, b>=a > For fixed z and a=-11/5, b=6





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









  


  










Input Form





Hypergeometric2F1[-(11/5), 6, 19/5, -z] == (1/(2441406250 z^(14/5))) (21 (-1)^(1/5) (132 (-1)^(4/5) (99 - 880 z + 9240 z^2 + 240240 z^3 + 620620 z^4 + 406224 z^5) Log[1 + z^(1/5)] + 132 (99 - 880 z + 9240 z^2 + 240240 z^3 + 620620 z^4 + 406224 z^5) Log[1 - (-1)^(1/5) z^(1/5)] - (-1)^(1/5) (132 (99 - 880 z + 9240 z^2 + 240240 z^3 + 620620 z^4 + 406224 z^5) Log[1 + (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (-132 (99 - 880 z + 9240 z^2 + 240240 z^3 + 620620 z^4 + 406224 z^5) Log[1 - (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-3267 + 30492 z + 22932728 z^2 + 72984912 z^3 + 53621568 z^4) + 132 (99 - 880 z + 9240 z^2 + 240240 z^3 + 620620 z^4 + 406224 z^5) Log[1 + (-1)^(4/5) z^(1/5)])))))










Standard Form





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MathML Form







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type='integer'> 53621568 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 72984912 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 22932728 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 30492 </cn> <ci> z </ci> </apply> <cn type='integer'> -3267 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 406224 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 620620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 240240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 880 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 99 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 406224 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 620620 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 240240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 880 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 99 </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> </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