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ArcCsc






Mathematica Notation

Traditional Notation









Elementary Functions > ArcCsc[z] > Transformations > Related transformations > Sums involving the direct function > Involving coth-1(z)





http://functions.wolfram.com/01.17.16.0147.01









  


  










Input Form





ArcCsc[x] + ArcCoth[y] == -2 I Pi (Floor[(-Arg[1/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])] - (1/2) Arg[1 + 1/y] + Pi)/(2 Pi)] + Floor[(Pi - Im[Log[1/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])]])/ (2 Pi)] + Floor[(Pi - (1/2) Im[Log[1 + 1/y]])/(2 Pi)]) - 2 I Pi (Floor[(-Arg[(Sqrt[1 - 1/x^2] + I/x)^(-I)] + (1/2) Arg[1 - 1/y] + Pi)/(2 Pi)] + Floor[((1/2) Im[Log[1 - 1/y]] + Pi)/(2 Pi)] + Floor[(Re[Log[Sqrt[1 - 1/x^2] + I/x]] + Pi)/(2 Pi)]) + I Pi (1 - (-1)^(Floor[-(Arg[Sqrt[1 + 1/y]/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y]) + 1]/(2 Pi))] - Floor[-(Arg[Sqrt[1 + 1/y]/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])]/ (2 Pi))])) + I (-1)^(Floor[Arg[Sqrt[1 + 1/y]/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y]) - 1]/(2 Pi) - Arg[Sqrt[1 + 1/y]/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y]) + 1]/(2 Pi) + 1/2] + Floor[-(Arg[Sqrt[1 + 1/y]/((Sqrt[1 - 1/x^2] + I/x)^I Sqrt[1 - 1/y])]/ Pi)]) (ArcCsc[(2 Sqrt[1 + 1/y])/((Sqrt[1 - 1/x^2] + I/x)^I (((1 + 1/y)/((Sqrt[1 - 1/x^2] + I/x)^(2 I) (1 - 1/y)) + 1) Sqrt[1 - 1/y]))] - Pi/2)










Standard Form





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MathML Form







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type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <arccsc /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> 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<imaginaryi /> <apply> <power /> <ci> x </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -2 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> y </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </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





© 1998- Wolfram Research, Inc.