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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, b>=a > For fixed z and a=1, b=25/8





http://functions.wolfram.com/07.23.03.c1s1.01









  


  








Input Form





Hypergeometric2F1[1, 25/8, 41/8, -z] == -((1/(3264 z^(33/8))) (11 (-1)^(1/8) (30600 (-1)^(7/8) z^(1/8) + 27200 (-1)^(7/8) z^(9/8) - 1600 (-1)^(7/8) z^(17/8) + 576 (-1)^(7/8) z^(25/8) + 3825 (-1)^(3/4) (1 + z) Log[1 - (-1)^(1/8) z^(1/8)] - 3825 (-1)^(3/4) (1 + z) Log[1 + (-1)^(1/8) z^(1/8)] + 3825 I Log[1 - (-1)^(3/8) z^(1/8)] + 3825 I z Log[1 - (-1)^(3/8) z^(1/8)] - 3825 I Log[1 + (-1)^(3/8) z^(1/8)] - 3825 I z Log[1 + (-1)^(3/8) z^(1/8)] + 3825 (-1)^(1/4) Log[1 - (-1)^(5/8) z^(1/8)] + 3825 (-1)^(1/4) z Log[1 - (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/4) Log[1 + (-1)^(5/8) z^(1/8)] - 3825 (-1)^(1/4) z Log[1 + (-1)^(5/8) z^(1/8)] + 3825 Log[1 - (-1)^(7/8) z^(1/8)] + 3825 z Log[1 - (-1)^(7/8) z^(1/8)] - 3825 Log[1 + (-1)^(7/8) z^(1/8)] - 3825 z Log[1 + (-1)^(7/8) z^(1/8)])))








Standard Form





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MathML Form







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</mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 8 </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> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='integer'> 1 </cn> <cn type='rational'> 25 <sep /> 8 </cn> </list> <list> <cn type='rational'> 41 <sep /> 8 </cn> </list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 3264 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 33 <sep /> 8 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <power 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Rule Form





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





2007-05-02