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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=-3/8, b>=a > For fixed z and a=-3/8, b=1





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









  


  








Input Form





Hypergeometric2F1[-(3/8), 1, 5/8, -z] == (-(1/8)) (-1)^(1/8) (8 (-1)^(7/8) - 3 (-1)^(1/4) z^(3/8) Log[1 - (-1)^(1/8) z^(1/8)] + 3 (-1)^(1/4) z^(3/8) Log[1 + (-1)^(1/8) z^(1/8)] + 3 z^(3/8) Log[1 - (-1)^(3/8) z^(1/8)] - 3 z^(3/8) Log[1 + (-1)^(3/8) z^(1/8)] + 3 (-1)^(3/4) z^(3/8) Log[1 - (-1)^(5/8) z^(1/8)] - 3 (-1)^(3/4) z^(3/8) Log[1 + (-1)^(5/8) z^(1/8)] - 3 I z^(3/8) Log[1 - (-1)^(7/8) z^(1/8)] + 3 I z^(3/8) Log[1 + (-1)^(7/8) z^(1/8)])








Standard Form





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MathML Form







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<power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 8 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <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> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 7 <sep /> 8 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02