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ArcTanh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.27.16.0212.01









  


  










Input Form





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










Standard Form





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MathML Form







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<cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> x </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02