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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=1, b>=a > For fixed z and a=1, b=2





http://functions.wolfram.com/07.23.03.az4u.01









  


  








Input Form





Hypergeometric2F1[1, 2, -(21/5), z] == (1/(9240 (1 - z)^7 (-1 + z)^7)) (24024 (1 - z)^(38/5) z^(22/5) + 24024 (1 - z)^(3/5) (-1 + z)^7 z^(22/5) - 24024 (-1 + z)^7 z^5 + (1 - z)^8 (-9240 + 69080 z - 228965 z^2 + 452175 z^3 - 647775 z^4 + 1758117 z^5 + 48048 z^6) + (1 - z)^7 z (-9240 + 69080 z - 228965 z^2 + 452175 z^3 - 623751 z^4 + 1758117 z^5 + 48048 z^6)) + (403 Sqrt[2 (5 + Sqrt[5])] z^(26/5) 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))])/(25 (1 - z)^(36/5)) + (403 Sqrt[10 - 2 Sqrt[5]] z^(26/5) 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))])/(25 (1 - z)^(36/5)) + (806 z^(26/5) Log[1 + z^(1/5)/(1 - z)^(1/5)])/(25 (1 - z)^(36/5)) + (403 (-1 + Sqrt[5]) z^(26/5) Log[1 - ((1 - Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(50 (1 - z)^(36/5)) - (403 (1 + Sqrt[5]) z^(26/5) Log[1 - ((1 + Sqrt[5]) z^(1/5))/(2 (1 - z)^(1/5)) + z^(2/5)/(1 - z)^(2/5)])/(50 (1 - z)^(36/5))








Standard Form





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MathML Form







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





2007-05-02