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ArcTanh






Mathematica Notation

Traditional Notation









Elementary Functions > ArcTanh[z] > Transformations > Related transformations > Linear combinations involving the direct function > Involving sec-1(z)





http://functions.wolfram.com/01.27.16.0221.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> </apply> <apply> <times /> <ci> a </ci> <imaginaryi /> <pi /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <arg /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <pi /> <apply> <plus /> <apply> <floor /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <arg /> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> 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Rule Form





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





2007-05-02