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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 8 and fixed z and a>0 > For fixed z and a=31/8, b>=a > For fixed z and a=31/8, b=4





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









  


  








Input Form





Hypergeometric2F1[31/8, 4, 47/8, -z] == (1/65536) (403 (-((128 (11 + 15 z))/(1 + z)^2) + (1/z^(31/8)) (-2760 z^(7/8) + 1288 z^(15/8) - 840 z^(23/8) + 2415 (-1)^(1/8) Log[1 - (-1)^(1/8) z^(1/8)] - 2415 (-1)^(1/8) Log[1 + (-1)^(1/8) z^(1/8)] + 2415 (-1)^(3/8) Log[1 - (-1)^(3/8) z^(1/8)] - 2415 (-1)^(3/8) Log[1 + (-1)^(3/8) z^(1/8)] + 2415 (-1)^(5/8) Log[1 - (-1)^(5/8) z^(1/8)] - 2415 (-1)^(5/8) Log[1 + (-1)^(5/8) z^(1/8)] + 2415 (-1)^(7/8) Log[1 - (-1)^(7/8) z^(1/8)] - 2415 (-1)^(7/8) Log[1 + (-1)^(7/8) z^(1/8)]) + 10695 (-(8/(7 z^4)) + 8/(15 z^3) - 8/(23 z^2) + 8/(31 z) + (1/z^(39/8)) ((-1)^(1/8) (Log[1 - (-1)^(1/8) z^(1/8)] - Log[1 + (-1)^(1/8) z^(1/8)] + (-1)^(1/4) Log[1 - (-1)^(3/8) z^(1/8)] - (-1)^(1/4) Log[1 + (-1)^(3/8) z^(1/8)] + I Log[1 - (-1)^(5/8) z^(1/8)] - I Log[1 + (-1)^(5/8) z^(1/8)] + (-1)^(3/4) Log[1 - (-1)^(7/8) z^(1/8)] - (-1)^(3/4) Log[1 + (-1)^(7/8) z^(1/8)])))))








Standard Form





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MathML Form







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</mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mfrac> <mn> 8 </mn> <mrow> <mn> 31 </mn> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mrow> <mn> 23 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mfrac> <mn> 8 </mn> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mn> 8 </mn> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 31 <sep /> 8 </cn> <cn type='integer'> 4 </cn> </list> <list> <cn type='rational'> 47 <sep /> 8 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z 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z </ci> <cn type='rational'> 15 <sep /> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2760 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 8 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2415 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </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'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2415 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2415 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </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'> 3 <sep /> 8 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2415 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn 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</math>










Rule Form





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





2007-05-02