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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 power function > Involving power > Linear argument





http://functions.wolfram.com/06.37.21.0007.01









  


  








Input Form





Integrate[SinIntegral[a z]/z, z] == (1/2) (a z HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, (-I) a z] + a z HypergeometricPFQ[{1, 1, 1}, {2, 2, 2}, I a z] - I Log[z] (Gamma[0, (-I) a z] - Gamma[0, I a z] + Log[(-I) a z] - Log[I a z] + 2 I SinIntegral[a z]))








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["SinIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]], "z_"], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", "z", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", "2"]], "}"]], ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "z"]]]], "]"]]]], "+", RowBox[List["a", " ", "z", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List["1", ",", "1", ",", "1"]], "}"]], ",", RowBox[List["{", RowBox[List["2", ",", "2", ",", "2"]], "}"]], ",", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]]]], "]"]]]], "-", RowBox[List["\[ImaginaryI]", " ", RowBox[List["Log", "[", "z", "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["0", ",", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]]]], "]"]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "z"]], "]"]], "-", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]], "]"]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]


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





2001-10-29