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SinhIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinhIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions > Involving Ci





http://functions.wolfram.com/06.39.21.0062.01









  


  










Input Form





Integrate[CosIntegral[b z] SinhIntegral[a z], z] == (1/(2 a b)) ((I a + b) CoshIntegral[(a - I b) z] + ((-I) a + b) CoshIntegral[(a + I b) z] - 2 (a Sin[b z] SinhIntegral[a z] + b CosIntegral[b z] (Cosh[a z] - a z SinhIntegral[a z])))










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a", " ", "b"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["CosIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["CosIntegral", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["\[ImaginaryI]", " ", "b"]]]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["CosIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]], "-", RowBox[List["a", " ", "z", " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]]]], RowBox[List["2", " ", "a", " ", "b"]]]]]]]










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





2001-10-29