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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.b2jn.01









  


  








Input Form





Hypergeometric2F1[3, 5, -(24/5), z] == -((1/(7125000 (-1 + z)^12)) (-7125000 + 107765625 z - 807750000 z^2 + 4173750000 z^3 - 18534687500 z^4 + 105668390625 z^5 + 384881425572 z^6 + 148437764630 z^7 + 3507004800 z^8 - 91328250 z^9)) + (1/(78125 (1 - z)^(64/5))) (10363353 Sqrt[(1/2) (5 + Sqrt[5])] z^(29/5) (221 + 260 z + 50 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)^(64/5))) (10363353 Sqrt[(1/2) (5 - Sqrt[5])] z^(29/5) (221 + 260 z + 50 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))]) - (10363353 z^(29/5) (221 + 260 z + 50 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/ (78125 (1 - z)^(64/5)) - (10363353 (-1 + Sqrt[5]) z^(29/5) (221 + 260 z + 50 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/ (2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(312500 (1 - z)^(64/5)) + (10363353 (1 + Sqrt[5]) z^(29/5) (221 + 260 z + 50 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(312500 (1 - z)^(64/5))








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