html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 SinIntegral

 http://functions.wolfram.com/06.37.21.0032.01

 Input Form

 Integrate[z^2 Cos[b z] SinIntegral[a z], z] == (1/(2 b^3)) ((1/((a - b)^2 (a + b)^2)) ((a^2 - b^2)^2 (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + 2 Cos[b z] (2 a b (a^2 - 2 b^2) Cos[a z] + b^3 (-a^2 + b^2) z Sin[a z]) - 2 b^2 (a (-a^2 + b^2) z Cos[a z] - (a^2 - 3 b^2) Sin[a z]) Sin[b z]) + I (Gamma[3, (-I) b z] - Gamma[3, I b z]) SinIntegral[a z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SuperscriptBox["b", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 z 2 cos ( b z ) Si ( a z ) z 1 2 b 3 ( 1 ( a - b ) 2 ( a + b ) 2 ( - 2 ( a ( b 2 - a 2 ) z cos ( a z ) - ( a 2 - 3 b 2 ) sin ( a z ) ) sin ( b z ) b 2 + ( a 2 - b 2 ) 2 ( Ei ( - ( a - b ) z ) + Ei ( ( a - b ) z ) - Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) ) + 2 cos ( b z ) ( ( b 2 - a 2 ) z sin ( a z ) b 3 + 2 a ( a 2 - 2 b 2 ) cos ( a z ) b ) ) + ( Γ ( 3 , - b z ) - Γ ( 3 , b z ) ) Si ( a z ) ) z z 2 b z SinIntegral a z 1 2 b 3 -1 1 a -1 b 2 a b 2 -1 -2 a b 2 -1 a 2 z a z -1 a 2 -1 3 b 2 a z b z b 2 a 2 -1 b 2 2 ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z -1 ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z 2 b z b 2 -1 a 2 z a z b 3 2 a a 2 -1 2 b 2 a z b Gamma 3 -1 b z -1 Gamma 3 b z SinIntegral a z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", "2"], " ", RowBox[List["Cos", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]], ")"]], "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], "2"]]]], "+", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "b", " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List["\[ImaginaryI]", " ", "b", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], RowBox[List["2", " ", SuperscriptBox["b", "3"]]]]]]]]

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

 2001-10-29