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SinIntegral




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function > Involving exp





http://functions.wolfram.com/06.37.21.0012.01









  


  








Input Form





Integrate[E^(I a z) SinIntegral[a z], z] == (1/(2 a)) (ExpIntegralEi[2 I a z] - Log[a z] - 2 I E^(I a z) SinIntegral[a z])








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a"]]], RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["a", " ", "z"]], "]"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "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> <mo> &#8747; </mo> <mrow> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> Si </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mfrac> <mrow> <mrow> <mi> Ei </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> Si </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> SinIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "a_", " ", "z_"]]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["2", " ", "\[ImaginaryI]", " ", "a", " ", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["a", " ", "z"]], "]"]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], RowBox[List["2", " ", "a"]]]]]]]


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





2001-10-29