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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=1/8, b>=a > For fixed z and a=1/8, b=2





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









  


  










Input Form





Hypergeometric2F1[1/8, 2, 25/8, z] == (1/(8192 z^(17/8))) (153 (-1)^(1/4) (-72 (-1)^(3/4) z^(1/8) + 8 (-1)^(3/4) z^(9/8) + (-1)^(3/4) (-9 + 2 z + 7 z^2) Log[1 - z^(1/8)] + (-1)^(1/4) (-9 + 2 z + 7 z^2) Log[1 - I z^(1/8)] + 9 (-1)^(1/4) Log[1 + I z^(1/8)] - 2 (-1)^(1/4) z Log[1 + I z^(1/8)] - 7 (-1)^(1/4) z^2 Log[1 + I z^(1/8)] + 9 (-1)^(3/4) Log[1 + z^(1/8)] - 2 (-1)^(3/4) z Log[1 + z^(1/8)] - 7 (-1)^(3/4) z^2 Log[1 + z^(1/8)] - 9 I Log[1 - (-1)^(1/4) z^(1/8)] + 2 I z Log[1 - (-1)^(1/4) z^(1/8)] + 7 I z^2 Log[1 - (-1)^(1/4) z^(1/8)] + 9 I Log[1 + (-1)^(1/4) z^(1/8)] - 2 I z Log[1 + (-1)^(1/4) z^(1/8)] - 7 I z^2 Log[1 + (-1)^(1/4) z^(1/8)] - 9 Log[1 - (-1)^(3/4) z^(1/8)] + 2 z Log[1 - (-1)^(3/4) z^(1/8)] + 7 z^2 Log[1 - (-1)^(3/4) z^(1/8)] + 9 Log[1 + (-1)^(3/4) z^(1/8)] - 2 z Log[1 + (-1)^(3/4) z^(1/8)] - 7 z^2 Log[1 + (-1)^(3/4) z^(1/8)]))










Standard Form





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MathML Form







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<mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> <mo> &#8290; </mo> <mroot> <mi> z </mi> <mn> 8 </mn> </mroot> </mrow> <mo> + </mo> <mn> 1 </mn> </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'> 1 <sep /> 8 </cn> <cn type='integer'> 2 </cn> </list> <list> <cn type='rational'> 25 <sep /> 8 </cn> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 8192 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 153 </cn> 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<cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -9 </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 /> 8 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> <cn type='integer'> -9 </cn> </apply> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> 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Rule Form





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





2007-05-02