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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.ap95.01









  


  










Input Form





Hypergeometric2F1[-(26/5), 4, -(6/5), z] == (1/234375) (234375 + 4062500 z + 213281250 z^2 - 1618802640 z^3 + 3180056880 z^4 - 1832070240 z^5 - 48048 z^(11/5) (-1456 + 8463 z - 14508 z^2 + 7626 z^3) Log[1 - z^(1/5)] + 48048 (-1)^(1/5) z^(11/5) (-1456 + 8463 z - 14508 z^2 + 7626 z^3) Log[1 + (-1)^(1/5) z^(1/5)] + 69957888 (-1)^(2/5) z^(11/5) Log[1 - (-1)^(2/5) z^(1/5)] - 406630224 (-1)^(2/5) z^(16/5) Log[1 - (-1)^(2/5) z^(1/5)] + 697080384 (-1)^(2/5) z^(21/5) Log[1 - (-1)^(2/5) z^(1/5)] - 366414048 (-1)^(2/5) z^(26/5) Log[1 - (-1)^(2/5) z^(1/5)] - 69957888 (-1)^(3/5) z^(11/5) Log[1 + (-1)^(3/5) z^(1/5)] + 406630224 (-1)^(3/5) z^(16/5) Log[1 + (-1)^(3/5) z^(1/5)] - 697080384 (-1)^(3/5) z^(21/5) Log[1 + (-1)^(3/5) z^(1/5)] + 366414048 (-1)^(3/5) z^(26/5) Log[1 + (-1)^(3/5) z^(1/5)] + 69957888 (-1)^(4/5) z^(11/5) Log[1 - (-1)^(4/5) z^(1/5)] - 406630224 (-1)^(4/5) z^(16/5) Log[1 - (-1)^(4/5) z^(1/5)] + 697080384 (-1)^(4/5) z^(21/5) Log[1 - (-1)^(4/5) z^(1/5)] - 366414048 (-1)^(4/5) z^(26/5) Log[1 - (-1)^(4/5) z^(1/5)])










Standard Form





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MathML Form







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type='integer'> 366414048 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 26 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1832070240 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 697080384 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 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</cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 16 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 406630224 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <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> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 16 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 406630224 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> 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/> <cn type='integer'> 8463 </cn> <ci> z </ci> </apply> <cn type='integer'> -1456 </cn> </apply> <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 /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 48048 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 7626 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 14508 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 8463 </cn> <ci> z </ci> </apply> <cn type='integer'> -1456 </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 /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 69957888 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn 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Rule Form





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





2007-05-02