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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=2, b>=a > For fixed z and a=2, b=5





http://functions.wolfram.com/07.23.03.b16j.01









  


  








Input Form





Hypergeometric2F1[2, 5, 16/5, z] == (11 (-108 + 270 z - 350 z^2 + 125 z^3))/(6250 (-1 + z)^3 z^2) - (99 Sqrt[2 (5 + Sqrt[5])] (-1 + z)^4 (-3 + 10 z) ArcTan[1 - ((1 - Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 + Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (15625 (1 - z)^(39/5) z^(11/5)) - (99 Sqrt[10 - 2 Sqrt[5]] (-1 + z)^4 (-3 + 10 z) ArcTan[1 - ((1 + Sqrt[5]) z^(1/5))/(4 (1 - z)^(1/5)), -((Sqrt[5/8 - Sqrt[5]/8] z^(1/5))/(1 - z)^(1/5))])/ (15625 (1 - z)^(39/5) z^(11/5)) + (198 (-1 + z)^4 (-3 + 10 z) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (15625 (1 - z)^(39/5) z^(11/5)) + (99 (-1 + Sqrt[5]) (-1 + z)^4 (-3 + 10 z) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(39/5) z^(11/5)) - (99 (1 + Sqrt[5]) (-1 + z)^4 (-3 + 10 z) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(31250 (1 - z)^(39/5) z^(11/5))








Standard Form





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MathML Form







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<power /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 15625 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 39 <sep /> 5 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 99 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 10 </cn> <apply> <times /> <cn type='integer'> -1 </cn> 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Rule Form





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





2007-05-02