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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Representations through equivalent functions > With inverse function





http://functions.wolfram.com/01.19.27.0069.01









  


  










Input Form





ArcSinh[Sinh[z]] == Piecewise[ {{(-1)^Floor[(2 Im[z] + Pi)/(2 Pi)] (-z + Pi I Floor[(2 Im[z] - Pi)/(2 Pi)]), Element[(2 Im[z] + Pi)/(2 Pi), Integers] && Re[z] >= 0}, {(-1)^Floor[(2 Im[z] + Pi)/(2 Pi)] (z - Pi I Floor[(2 Im[z] + Pi)/(2 Pi)]), True}}]










Standard Form





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MathML Form







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</mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mtd> <mtd> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> &#960; </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[List[], Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8805; </mo> <mn> 0 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> &#8970; 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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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