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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=-22/5, b>=a > For fixed z and a=-22/5, b=3





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









  


  










Input Form





Hypergeometric2F1[-(22/5), 3, -(7/5), -z] == (1/21875) (21875 - 206250 z + 3506250 z^2 + 18479340 z^3 + 16964640 z^4 + 15708 z^(12/5) (187 + 594 z + 432 z^2) Log[1 + z^(1/5)] + 15708 (-1)^(2/5) z^(12/5) (187 + 594 z + 432 z^2) Log[1 - (-1)^(1/5) z^(1/5)] + 2937396 (-1)^(4/5) z^(12/5) Log[1 + (-1)^(2/5) z^(1/5)] + 9330552 (-1)^(4/5) z^(17/5) Log[1 + (-1)^(2/5) z^(1/5)] + 6785856 (-1)^(4/5) z^(22/5) Log[1 + (-1)^(2/5) z^(1/5)] - 2937396 (-1)^(1/5) z^(12/5) Log[1 - (-1)^(3/5) z^(1/5)] - 9330552 (-1)^(1/5) z^(17/5) Log[1 - (-1)^(3/5) z^(1/5)] - 6785856 (-1)^(1/5) z^(22/5) Log[1 - (-1)^(3/5) z^(1/5)] - 2937396 (-1)^(3/5) z^(12/5) Log[1 + (-1)^(4/5) z^(1/5)] - 9330552 (-1)^(3/5) z^(17/5) Log[1 + (-1)^(4/5) z^(1/5)] - 6785856 (-1)^(3/5) z^(22/5) Log[1 + (-1)^(4/5) z^(1/5)])










Standard Form





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MathML Form







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type='rational'> 22 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16964640 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9330552 </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'> 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> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 9330552 </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'> 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type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15708 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 594 </cn> <ci> z </ci> </apply> <cn type='integer'> 187 </cn> </apply> <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> <power /> <ci> z </ci> <cn type='rational'> 12 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 15708 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 432 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 594 </cn> <ci> z </ci> </apply> <cn type='integer'> 187 </cn> </apply> <apply> <ln /> 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Rule Form





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





2007-05-02