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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=-26/5, b>=a > For fixed z and a=-26/5, b=4





http://functions.wolfram.com/07.23.03.ap9o.01









  


  










Input Form





Hypergeometric2F1[-(26/5), 4, 29/5, z] == (1/(152587890625 z^(24/5))) (19 (-1)^(1/5) (144144 (-1)^(4/5) (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - z^(1/5)] + 144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + (-1)^(1/5) (-144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - (-1)^(2/5) z^(1/5)] + (-1)^(1/5) (144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 + (-1)^(3/5) z^(1/5)] + (-1)^(1/5) (5 (-1)^(1/5) z^(4/5) (-4792788 + 7959952 z + 6358352 z^2 + 9081072 z^3 - 1573625973 z^4 + 5243050488 z^5 - 7566706602 z^6 + 5745496848 z^7 - 2262532272 z^8 + 366414048 z^9) - 144144 (-1 + z)^7 (133 + 651 z + 1674 z^2 + 2542 z^3) Log[1 - (-1)^(4/5) z^(1/5)])))))










Standard Form





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MathML Form







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type='integer'> 7566706602 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5243050488 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1573625973 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 9081072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6358352 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7959952 </cn> <ci> z </ci> </apply> <cn type='integer'> -4792788 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144144 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2542 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1674 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 651 </cn> <ci> z </ci> </apply> <cn type='integer'> 133 </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 144144 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 7 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2542 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1674 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 651 </cn> <ci> z </ci> </apply> <cn type='integer'> 133 </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> </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