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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=6, b>=a > For fixed z and a=6, b=6





http://functions.wolfram.com/07.23.03.b4kj.01









  


  










Input Form





Hypergeometric2F1[6, 6, 6/5, z] == (29 (5256581 + 66923380 z + 141922050 z^2 + 65994500 z^3 + 5074375 z^4))/ (244140625 (-1 + z)^10) - (4788 Sqrt[2 (5 + Sqrt[5])] (9576 + 299250 z + 1330000 z^2 + 1425000 z^3 + 375000 z^4 + 15625 z^5) 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))])/ (1220703125 (1 - z)^(54/5) z^(1/5)) - (4788 Sqrt[10 - 2 Sqrt[5]] (9576 + 299250 z + 1330000 z^2 + 1425000 z^3 + 375000 z^4 + 15625 z^5) 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))])/ (1220703125 (1 - z)^(54/5) z^(1/5)) + (9576 (9576 + 299250 z + 1330000 z^2 + 1425000 z^3 + 375000 z^4 + 15625 z^5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(1220703125 (1 - z)^(54/5) z^(1/5)) + (2394 (-1 + Sqrt[5]) (9576 + 299250 z + 1330000 z^2 + 1425000 z^3 + 375000 z^4 + 15625 z^5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(1220703125 (1 - z)^(54/5) z^(1/5)) - (2394 (1 + Sqrt[5]) (9576 + 299250 z + 1330000 z^2 + 1425000 z^3 + 375000 z^4 + 15625 z^5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/ (1220703125 (1 - z)^(54/5) z^(1/5))










Standard Form





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MathML Form







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type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 299250 </cn> <ci> z </ci> </apply> <cn type='integer'> 9576 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> <apply> <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'> 2 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 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Date Added to functions.wolfram.com (modification date)





2007-05-02