Hyperbolic cosecant: Representations through more general functions (formula 01.23.26.0022)

Csch

$Mathematica Notation$

Elementary Functions

Csch[z]

Representations through more general functions

Through other functions

Involving Jacobi functions

http://functions.wolfram.com/01.23.26.0022.01

Input Form

Csch[z] == I/JacobiSN[I z, 0]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "\[Equal]", FractionBox["\[ImaginaryI]", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", "0"]], "]"]]]]]]]

MathML Form

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mi> csch </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mfrac> <mi> ⅈ </mi> <mrow> <mi> sn </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ❘ </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <csch /> <ci> z </ci> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <ci> JacobiSN </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='integer'> 0 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox["\[ImaginaryI]", RowBox[List["JacobiSN", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "z"]], ",", "0"]], "]"]]]]]]]

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

2001-10-29