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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=3, b>=a > For fixed z and a=3, b=5





http://functions.wolfram.com/07.23.03.b2jv.01









  


  








Input Form





Hypergeometric2F1[3, 5, -(14/5), z] == -((1/(656250 (-1 + z)^10)) (-656250 + 10078125 z - 88125000 z^2 + 813125000 z^3 + 4796639134 z^4 + 2653847835 z^5 + 87939600 z^6 - 2892750 z^7)) + (1/(78125 (1 - z)^(54/5))) (730626 Sqrt[2 (5 + Sqrt[5])] z^(19/5) (174 + 290 z + 75 z^2) 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))) (730626 Sqrt[10 - 2 Sqrt[5]] z^(19/5) (174 + 290 z + 75 z^2) 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))]) - (1461252 z^(19/5) (174 + 290 z + 75 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(78125 (1 - z)^(54/5)) - (365313 (-1 + Sqrt[5]) z^(19/5) (174 + 290 z + 75 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(54/5)) + (365313 (1 + Sqrt[5]) z^(19/5) (174 + 290 z + 75 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(78125 (1 - z)^(54/5))








Standard Form





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MathML Form







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Rule Form





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





2007-05-02