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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=5, b>=a > For fixed z and a=5, b=6





http://functions.wolfram.com/07.23.03.b4bb.01









  


  








Input Form





Hypergeometric2F1[5, 6, -(19/5), z] == (1/(556640625 (-1 + z)^14)) (556640625 - 12187500000 z + 145136718750 z^2 - 1405742187500 z^3 + 17631660156250 z^4 + 202702403444968 z^5 + 325658687927090 z^6 + 135111275984900 z^7 + 12686004564125 z^8 + 60276645000 z^9) - (1/(48828125 (1 - z)^(74/5))) (41453412 Sqrt[2 (5 + Sqrt[5])] z^(24/5) (70499 + 243100 z + 214500 z^2 + 55000 z^3 + 3125 z^4) 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))]) - (1/(48828125 (1 - z)^(74/5))) (41453412 Sqrt[10 - 2 Sqrt[5]] z^(24/5) (70499 + 243100 z + 214500 z^2 + 55000 z^3 + 3125 z^4) 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))]) + (1/(48828125 (1 - z)^(74/5))) (82906824 z^(24/5) (70499 + 243100 z + 214500 z^2 + 55000 z^3 + 3125 z^4) Log[1 + z^(1/5)/(1 - z)^(1/5)]) + (1/(48828125 (1 - z)^(74/5))) (20726706 (-1 + Sqrt[5]) z^(24/5) (70499 + 243100 z + 214500 z^2 + 55000 z^3 + 3125 z^4) Log[1 - ((1 - Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(48828125 (1 - z)^(74/5))) (20726706 (1 + Sqrt[5]) z^(24/5) (70499 + 243100 z + 214500 z^2 + 55000 z^3 + 3125 z^4) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])








Standard Form





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MathML Form







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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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='rational'> 5 <sep /> 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> 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</apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 24 <sep /> 5 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 556640625 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 14 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 60276645000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 9 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 12686004564125 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 135111275984900 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 325658687927090 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> 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Rule Form





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





2007-05-02