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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 4 and fixed z > For fixed z and a=1, b>=a > For fixed z and a=1, b=6





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









  


  










Input Form





Hypergeometric2F1[1, 6, -(5/4), z] == (1/327680) ((1/(-1 + z)^8) (8 (40960 - 524288 z + 8224768 z^2 + 3516555 z^3 - 1676940 z^4 + 657120 z^5 - 162432 z^6 + 18432 z^7)) - (20188350 Sqrt[2] z^(9/4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(33/4) - (20188350 Sqrt[2] z^(9/4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))])/(1 - z)^(33/4) + (10094175 Sqrt[2] z^(9/4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(33/4) - (10094175 Sqrt[2] z^(9/4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]])/(1 - z)^(33/4))










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