Sine integral: Representations through equivalent functions (formula 06.37.27.0001)

SinIntegral

$Mathematica Notation$

Gamma, Beta, Erf

SinIntegral[z]

Representations through equivalent functions

With related functions

http://functions.wolfram.com/06.37.27.0001.01

Input Form

SinIntegral[z] == (-I) SinhIntegral[I z]

Standard Form

Cell[BoxData[RowBox[List[RowBox[List["SinIntegral", "[", "z", "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["SinhIntegral", "[", 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> Si </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ⁢ </mo> <mrow> <mi> Shi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ⅈ </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> SinIntegral </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <ci> SinhIntegral </ci> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Rule Form

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SinIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]]]]]]

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

2001-10-29