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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=4





http://functions.wolfram.com/07.23.03.b2fv.01









  


  








Input Form





Hypergeometric2F1[3, 4, -(24/5), z] == (1/(2493750 (-1 + z)^11)) (-2493750 + 33665625 z - 222140625 z^2 + 993421875 z^3 - 3740281250 z^4 + 17684065625 z^5 + 47362651421 z^6 + 12192852775 z^7 + 127859550 z^8) + (1/(15625 (1 - z)^(59/5))) (422994 Sqrt[2 (5 + Sqrt[5])] z^(29/5) (221 + 195 z + 25 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/(15625 (1 - z)^(59/5))) (422994 Sqrt[10 - 2 Sqrt[5]] z^(29/5) (221 + 195 z + 25 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))]) - (845988 z^(29/5) (221 + 195 z + 25 z^2) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(15625 (1 - z)^(59/5)) - (211497 (-1 + Sqrt[5]) z^(29/5) (221 + 195 z + 25 z^2) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(59/5)) + (211497 (1 + Sqrt[5]) z^(29/5) (221 + 195 z + 25 z^2) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(15625 (1 - z)^(59/5))








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