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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=-23/5, b>=a > For fixed z and a=-23/5, b=3





http://functions.wolfram.com/07.23.03.aq12.01









  


  








Input Form





Hypergeometric2F1[-(23/5), 3, -(3/5), -z] == (1/15625) (15625 - 359375 z - 4369770 z^2 - 9481290 z^3 - 5525520 z^4 + 21528 z^(8/5) (39 + 207 z + 322 z^2 + 154 z^3) Log[1 + z^(1/5)] - 21528 (-1)^(3/5) z^(8/5) (39 + 207 z + 322 z^2 + 154 z^3) Log[1 - (-1)^(1/5) z^(1/5)] - 839592 (-1)^(1/5) z^(8/5) Log[1 + (-1)^(2/5) z^(1/5)] - 4456296 (-1)^(1/5) z^(13/5) Log[1 + (-1)^(2/5) z^(1/5)] - 6932016 (-1)^(1/5) z^(18/5) Log[1 + (-1)^(2/5) z^(1/5)] - 3315312 (-1)^(1/5) z^(23/5) Log[1 + (-1)^(2/5) z^(1/5)] + 839592 (-1)^(4/5) z^(8/5) Log[1 - (-1)^(3/5) z^(1/5)] + 4456296 (-1)^(4/5) z^(13/5) Log[1 - (-1)^(3/5) z^(1/5)] + 6932016 (-1)^(4/5) z^(18/5) Log[1 - (-1)^(3/5) z^(1/5)] + 3315312 (-1)^(4/5) z^(23/5) Log[1 - (-1)^(3/5) z^(1/5)] + 839592 (-1)^(2/5) z^(8/5) Log[1 + (-1)^(4/5) z^(1/5)] + 4456296 (-1)^(2/5) z^(13/5) Log[1 + (-1)^(4/5) z^(1/5)] + 6932016 (-1)^(2/5) z^(18/5) Log[1 + (-1)^(4/5) z^(1/5)] + 3315312 (-1)^(2/5) z^(23/5) Log[1 + (-1)^(4/5) z^(1/5)])








Standard Form





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MathML Form







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</mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 23 <sep /> 5 </cn> </apply> <cn type='integer'> 3 </cn> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 15625 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -3315312 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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 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</apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 154 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 322 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 207 </cn> <ci> z </ci> </apply> <cn type='integer'> 39 </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'> 8 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 5 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 154 </cn> <apply> <power /> <ci> z </ci> <cn 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Rule Form





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





2007-05-02