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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=1





http://functions.wolfram.com/07.23.03.apx7.01









  


  








Input Form





Hypergeometric2F1[-(23/5), 1, -(8/5), z] == (1/1000) (1000 + 2875 z + 17250 z^2 - 58305 z^3 + 35880 z^4 + 21528 (-1 + z)^2 z^(13/5) Log[1 - z^(1/5)] - 21528 (-1)^(3/5) (-1 + z)^2 z^(13/5) Log[1 + (-1)^(1/5) z^(1/5)] - 21528 (-1)^(1/5) z^(13/5) Log[1 - (-1)^(2/5) z^(1/5)] + 43056 (-1)^(1/5) z^(18/5) Log[1 - (-1)^(2/5) z^(1/5)] - 21528 (-1)^(1/5) z^(23/5) Log[1 - (-1)^(2/5) z^(1/5)] + 21528 (-1)^(4/5) z^(13/5) Log[1 + (-1)^(3/5) z^(1/5)] - 43056 (-1)^(4/5) z^(18/5) Log[1 + (-1)^(3/5) z^(1/5)] + 21528 (-1)^(4/5) z^(23/5) Log[1 + (-1)^(3/5) z^(1/5)] + 21528 (-1)^(2/5) z^(13/5) Log[1 - (-1)^(4/5) z^(1/5)] - 43056 (-1)^(2/5) z^(18/5) Log[1 - (-1)^(4/5) z^(1/5)] + 21528 (-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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</ci> <cn type='rational'> 23 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 23 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 43056 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 5 </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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 43056 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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 </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 43056 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 18 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 58305 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </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 /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <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> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <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 </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </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'> 1 <sep /> 5 </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'> 2 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 4 <sep /> 5 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <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 </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 21528 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 2 <sep /> 5 </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'> 4 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17250 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2875 </cn> <ci> z </ci> </apply> <cn type='integer'> 1000 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02