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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=5





http://functions.wolfram.com/07.23.03.b3kz.01









  


  








Input Form





Hypergeometric2F1[4, 5, -(9/5), z] == (1/(703125 (-1 + z)^10)) (703125 - 14843750 z + 256250000 z^2 + 3150618264 z^3 + 4002405955 z^4 + 866143850 z^5 + 8678250 z^6) - (1/(390625 (1 - z)^(54/5))) (262276 Sqrt[2 (5 + Sqrt[5])] z^(14/5) (1102 + 3480 z + 2175 z^2 + 250 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/(390625 (1 - z)^(54/5))) (262276 Sqrt[10 - 2 Sqrt[5]] z^(14/5) (1102 + 3480 z + 2175 z^2 + 250 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))]) + (524552 z^(14/5) (1102 + 3480 z + 2175 z^2 + 250 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(390625 (1 - z)^(54/5)) + (1/(390625 (1 - z)^(54/5))) (131138 (-1 + Sqrt[5]) z^(14/5) (1102 + 3480 z + 2175 z^2 + 250 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) - (1/(390625 (1 - z)^(54/5))) (131138 (1 + Sqrt[5]) z^(14/5) (1102 + 3480 z + 2175 z^2 + 250 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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<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> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 14 <sep /> 5 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 390625 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> 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Rule Form





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





2007-05-02