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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=5, b>=a > For fixed z and a=5, b=6





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









  


  










Input Form





Hypergeometric2F1[5, 6, -(13/4), z] == (1/5234491392) ((1/(-1 + z)^14) (8 (654311424 - 15200157696 z + 200470953984 z^2 - 2418804785152 z^3 + 80379222425600 z^4 + 455756277037691 z^5 + 565591892560996 z^6 + 197041628215456 z^7 + 15746091793792 z^8 + 45480314880 z^9)) - (1/(1 - z)^(57/4)) (8216658450 Sqrt[2] z^(17/4) (33495 + 127600 z + 122496 z^2 + 33792 z^3 + 2048 z^4) ArcTan[1 - z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) - (1/(1 - z)^(57/4)) (8216658450 Sqrt[2] z^(17/4) (33495 + 127600 z + 122496 z^2 + 33792 z^3 + 2048 z^4) ArcTan[1 + z^(1/4)/(Sqrt[2] (1 - z)^(1/4)), -(z^(1/4)/(Sqrt[2] (1 - z)^(1/4)))]) + (1/(1 - z)^(57/4)) (4108329225 Sqrt[2] z^(17/4) (33495 + 127600 z + 122496 z^2 + 33792 z^3 + 2048 z^4) Log[1 - (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]) - (1/(1 - z)^(57/4)) (4108329225 Sqrt[2] z^(17/4) (33495 + 127600 z + 122496 z^2 + 33792 z^3 + 2048 z^4) Log[1 + (Sqrt[2] z^(1/4))/(1 - z)^(1/4) + Sqrt[z]/Sqrt[1 - z]]))










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