InverseLaplaceTransform[ArcCoth[t], t, z] == Sinh[z]/z

Cell[BoxData[RowBox[List[RowBox[List["InverseLaplaceTransform", "[", RowBox[List[RowBox[List["ArcCoth", "[", "t", "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List["Sinh", "[", "z", "]"]], "z"]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msubsup> <mi> &#8466; </mi> <mi> t </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> [ </mo> <mrow> <msup> <mi> coth </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mi> t </mi> <mo> ) </mo> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mi> z </mi> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> InverseLaplaceTransform </ci> <apply> <arccoth /> <ci> t </ci> </apply> <ci> t </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <sinh /> <ci> z </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["InverseLaplaceTransform", "[", RowBox[List[RowBox[List["ArcCoth", "[", "t_", "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["Sinh", "[", "z", "]"]], "z"]]]]]

2001-10-29