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SinIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Representations through more general functions > Through other functions





http://functions.wolfram.com/06.37.26.0017.01









  


  








Input Form





SinIntegral[z] == (I/2) (Gamma[0, (-I) z] - Gamma[0, I z] + Log[(-I) z] - Log[I z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["SinIntegral", "[", "z", "]"]], "\[Equal]", RowBox[List[FractionBox["\[ImaginaryI]", "2"], RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "]"]], "-", RowBox[List["Log", "[", 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> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mi> &#8520; </mi> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 0 </mn> <mo> , </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </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 /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <ci> Gamma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Gamma </ci> <cn type='integer'> 0 </cn> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> <apply> <ln /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <imaginaryi /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SinIntegral", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["\[ImaginaryI]", " ", "z"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", "z"]], "]"]]]], ")"]]]]]]]]


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





2001-10-29