Cosecant: Representations through more general functions (formula 01.10.26.0005)

Csc

$Mathematica Notation$

Elementary Functions

Csc[z]

Representations through more general functions

Through other functions

Involving Bessel functions

http://functions.wolfram.com/01.10.26.0005.01

Input Form

Csc[z] == Sqrt[2/Pi] (I/(Sqrt[I z] BesselI[1/2, I z]))

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["Csc", "[", "z", "]"]], "\[Equal]", RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], FractionBox["\[ImaginaryI]", RowBox[List[" ", RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "z"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["\[ImaginaryI]", " ", "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> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <msqrt> <mfrac> <mn> 2 </mn> <mi> π </mi> </mfrac> </msqrt> <mo> ⁢ </mo> <mfrac> <mrow> <mtext> </mtext> <mi> ⅈ </mi> </mrow> <mrow> <msqrt> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <msub> <mi> I </mi> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </msub> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <csc /> <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 /> <imaginaryi /> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> BesselI </ci> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </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["Csc", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SqrtBox[FractionBox["2", "\[Pi]"]], " ", "\[ImaginaryI]"]], RowBox[List[SqrtBox[RowBox[List["\[ImaginaryI]", " ", "z"]]], " ", RowBox[List["BesselI", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]]]]]]]]]

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

2001-10-29