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ArcCosh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.26.16.0218.01









  


  










Input Form





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










Standard Form





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MathML Form







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<cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <imaginary /> <apply> <times /> <ci> a </ci> <apply> <ln /> <apply> <plus /> <ci> x </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <floor /> <apply> <times /> <apply> <plus /> <pi /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <real /> <apply> <times /> <ci> b </ci> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> x </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <imaginaryi /> <ci> y </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> </apply> </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





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