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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=6





http://functions.wolfram.com/07.23.03.b3o7.01









  


  








Input Form





Hypergeometric2F1[4, 6, -(24/5), z] == -((1/(74218750 (-1 + z)^14)) (-74218750 + 1410156250 z - 13658203125 z^2 + 94476562500 z^3 - 587056640625 z^4 + 4936066406250 z^5 + 34129462040877 z^6 + 31980395548560 z^7 + 6324696367725 z^8 + 89075486500 z^9 - 1674351250 z^10)) + (1/(9765625 (1 - z)^(74/5))) (186540354 Sqrt[2 (5 + Sqrt[5])] z^(29/5) (4862 + 10725 z + 5500 z^2 + 625 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/(9765625 (1 - z)^(74/5))) (186540354 Sqrt[10 - 2 Sqrt[5]] z^(29/5) (4862 + 10725 z + 5500 z^2 + 625 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))]) - (373080708 z^(29/5) (4862 + 10725 z + 5500 z^2 + 625 z^3) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(9765625 (1 - z)^(74/5)) - (1/(9765625 (1 - z)^(74/5))) (93270177 (-1 + Sqrt[5]) z^(29/5) (4862 + 10725 z + 5500 z^2 + 625 z^3) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)]) + (1/(9765625 (1 - z)^(74/5))) (93270177 (1 + Sqrt[5]) z^(29/5) (4862 + 10725 z + 5500 z^2 + 625 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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Date Added to functions.wolfram.com (modification date)





2007-05-02