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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=1, b>=a > For fixed z and a=1, b=6





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









  


  








Input Form





Hypergeometric2F1[1, 6, 2/5, z] == (4096 ((1 - z)^(4/5) - (1 - z)^(3/5) z^(1/5) + (1 - z)^(2/5) z^(2/5) - (1 - z)^(1/5) z^(3/5) + z^(4/5))^5 (15625 + 65277 z - 53820 z^2 + 33275 z^3 - 12000 z^4 + 1875 z^5))/(15625 ((1 - z)^(1/5) + z^(1/5)) (2 (1 - z)^(2/5) + (-1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^6 (2 (1 - z)^(2/5) - (1 + Sqrt[5]) (1 - z)^(1/5) z^(1/5) + 2 z^(2/5))^6 (-1 + z)^6) + (75348 Sqrt[10 - 2 Sqrt[5]] z^(3/5) 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))])/ (78125 (1 - z)^(33/5)) - (75348 Sqrt[2 (5 + Sqrt[5])] z^(3/5) 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))])/ (78125 (1 - z)^(33/5)) - (150696 z^(3/5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (78125 (1 - z)^(33/5)) + (37674 (1 + Sqrt[5]) z^(3/5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(33/5)) - (37674 (-1 + Sqrt[5]) z^(3/5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(33/5))








Standard Form





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MathML Form







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</mn> </mroot> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 78125 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 33 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mrow> </mfrac> <mo> - </mo> <mfrac> <mrow> <mn> 37674 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msqrt> <mn> 5 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 5 </mn> </mrow> </msup> </mfrac> <mo> - </mo> <mfrac> <mrow> 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type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 2 <sep /> 5 </cn> </apply> </apply> </apply> <cn type='integer'> 6 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </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'> 2 <sep /> 5 </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> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn 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/> 8 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <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'> 1 <sep /> 5 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 78125 </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'> 33 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> 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type='integer'> 2 </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'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 78125 </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'> 33 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 37674 </cn> <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'> 3 <sep /> 5 </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 </cn> <ci> z </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> 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Rule Form





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





2007-05-02