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ArcSech






Mathematica Notation

Traditional Notation









Elementary Functions > ArcSech[z] > Transformations > Related transformations > Linear combinations involving the direct function > Involving log(z)





http://functions.wolfram.com/01.30.16.0234.01









  


  










Input Form





a ArcSech[x] + b Log[y] == I Pi (1 - (-1)^(Floor[-(Arg[y^b (Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a + 1]/ (2 Pi))] - Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b]/ (2 Pi))])) + (-1)^(Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b]/Pi)] - Floor[-(Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b - 1]/(2 Pi))] + Floor[Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b]/Pi - (2 Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b - 1])/Pi] + Floor[-(Arg[y^b (Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a + 1]/(2 Pi))]) ArcSech[(2 (Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a y^b)/ (y^(2 b) (Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^(2 a) + 1)] - 2 I Pi (Floor[(-Arg[(Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x)^a] - Arg[y^b] + Pi)/ (2 Pi)] + Floor[(Pi - Im[a Log[Sqrt[1/x - 1] Sqrt[1 + 1/x] + 1/x]])/ (2 Pi)] + Floor[(Pi - Im[b Log[y]])/(2 Pi)])










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