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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=4, b>=a > For fixed z and a=4, b=4





http://functions.wolfram.com/07.23.03.b3h7.01









  


  








Input Form





Hypergeometric2F1[4, 4, -(14/5), z] == -((1/(984375 (-1 + z)^10)) (-984375 + 15468750 z - 139609375 z^2 + 1347812500 z^3 + 8770267833 z^4 + 5981974730 z^5 + 564981325 z^6)) + (1/(78125 (1 - z)^(54/5))) (37468 Sqrt[2 (5 + Sqrt[5])] z^(19/5) (3944 + 7395 z + 2550 z^2 + 125 z^3) 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/(78125 (1 - z)^(54/5))) (37468 Sqrt[10 - 2 Sqrt[5]] z^(19/5) (3944 + 7395 z + 2550 z^2 + 125 z^3) 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))]) - (74936 z^(19/5) (3944 + 7395 z + 2550 z^2 + 125 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(54/5)) - (1/(78125 (1 - z)^(54/5))) (18734 (-1 + Sqrt[5]) z^(19/5) (3944 + 7395 z + 2550 z^2 + 125 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(78125 (1 - z)^(54/5))) (18734 (1 + Sqrt[5]) z^(19/5) (3944 + 7395 z + 2550 z^2 + 125 z^3) 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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</cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2550 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7395 </cn> <ci> z </ci> </apply> <cn type='integer'> 3944 </cn> </apply> <apply> <arctan /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 5 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </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> </apply> 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type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 984375 </cn> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 10 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 564981325 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5981974730 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 8770267833 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1347812500 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <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