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Csch




Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Representations through more general functions > Through other functions > Involving some hypergeometric-type functions





http://functions.wolfram.com/01.23.26.0027.01









  


  








Input Form





Csch[z] == Sqrt[2/Pi]/(Sqrt[z] StruveL[-(1/2), z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["Csch", "[", "z", "]"]], "\[Equal]", FractionBox[SqrtBox[FractionBox["2", "\[Pi]"]], RowBox[List[" ", RowBox[List[SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]]]]]]]]








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> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <msqrt> <mfrac> <mn> 2 </mn> <mi> &#960; </mi> </mfrac> </msqrt> <mo> &#8290; </mo> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mi> z </mi> </msqrt> <mo> &#8290; </mo> <mrow> <msub> <mstyle fontweight='bold' fontstyle='normal'> <semantics> <mi> L </mi> <annotation-xml encoding='MathML-Content'> <ci> StruveL </ci> </annotation-xml> </semantics> </mstyle> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <csch /> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <pi /> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> StruveL </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Csch", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[SqrtBox[FractionBox["2", "\[Pi]"]], RowBox[List[SqrtBox["z"], " ", RowBox[List["StruveL", "[", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], ",", "z"]], "]"]]]]]]]]]


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





2001-10-29