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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=-4/5, b>=a > For fixed z and a=-4/5, b=1





http://functions.wolfram.com/07.23.03.aw3h.01









  


  










Input Form





Hypergeometric2F1[-(4/5), 1, 21/5, z] == (1/(9375 z^(16/5))) (4 (660 z^(1/5) - 2530 z^(6/5) + 3580 z^(11/5) + 165 z^(16/5) + 132 (-1 + z)^4 Log[1 - z^(1/5)] + 132 (-1)^(4/5) (-1 + z)^4 Log[1 + (-1)^(1/5) z^(1/5)] - 132 (-1)^(3/5) Log[1 - (-1)^(2/5) z^(1/5)] + 528 (-1)^(3/5) z Log[1 - (-1)^(2/5) z^(1/5)] - 792 (-1)^(3/5) z^2 Log[1 - (-1)^(2/5) z^(1/5)] + 528 (-1)^(3/5) z^3 Log[1 - (-1)^(2/5) z^(1/5)] - 132 (-1)^(3/5) z^4 Log[1 - (-1)^(2/5) z^(1/5)] + 132 (-1)^(2/5) Log[1 + (-1)^(3/5) z^(1/5)] - 528 (-1)^(2/5) z Log[1 + (-1)^(3/5) z^(1/5)] + 792 (-1)^(2/5) z^2 Log[1 + (-1)^(3/5) z^(1/5)] - 528 (-1)^(2/5) z^3 Log[1 + (-1)^(3/5) z^(1/5)] + 132 (-1)^(2/5) z^4 Log[1 + (-1)^(3/5) z^(1/5)] - 132 (-1)^(1/5) Log[1 - (-1)^(4/5) z^(1/5)] + 528 (-1)^(1/5) z Log[1 - (-1)^(4/5) z^(1/5)] - 792 (-1)^(1/5) z^2 Log[1 - (-1)^(4/5) z^(1/5)] + 528 (-1)^(1/5) z^3 Log[1 - (-1)^(4/5) z^(1/5)] - 132 (-1)^(1/5) z^4 Log[1 - (-1)^(4/5) z^(1/5)]))










Standard Form





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MathML Form







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type='integer'> 9375 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 16 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 132 </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> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 132 </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'> 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> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 165 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 16 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3580 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2530 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 6 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 132 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 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Rule Form





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





2007-05-02