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ArcCsc






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.17.16.0190.01









  


  










Input Form





ArcCsc[x] - I ArcSech[y] == -ArcCsc[ 1/((-1)^Floor[1/2 - Arg[I Sqrt[1 - 1/x^2] Sqrt[-1 + 1/y] Sqrt[1 + 1/y] - 1/(x y)]/Pi] (-((I Sqrt[-1 + 1/y] Sqrt[1 + 1/y])/x) - Sqrt[1 - 1/x^2]/y))] - (1/2) Pi ((-(1/2)) (1 + (-1)^(-Floor[-(Arg[1 - 1/y]/(2 Pi))])) ((-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] + 1/(x y)]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] + 1/(x y)]/ Pi]) Floor[(Arg[Sqrt[1 - 1/x^2] - I/x] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] + 1/(x y)]/ Pi]) Floor[1/2 - (Arg[Sqrt[1 - 1/x^2] - I/x] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)]) + (1/2) (1 - (-1)^(-Floor[-(Arg[1 - 1/y]/(2 Pi))])) ((-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] - 1/(x y)]/Pi] + 2 (-1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] - 1/(x y)]/ Pi]) Floor[(Arg[Sqrt[1 - 1/x^2] + I/x] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)] + 2 (1 + (-1)^Floor[1/2 - Arg[Sqrt[1 - 1/x^2] Sqrt[1 - 1/y^2] - 1/(x y)]/ Pi]) Floor[1/2 - (Arg[Sqrt[1 - 1/x^2] + I/x] + Arg[Sqrt[1 - 1/y^2] + I/y])/(2 Pi)]))










Standard Form





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MathML Form







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





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





2007-05-02





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