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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function, exponential and a power functions > Involving products of powers of the direct function, exponential and a power functions > Involving product of power of the direct function, the direct function, exponential and a power functions > Involving zalpha-1eb zsin(c z) sinnu(a z)





http://functions.wolfram.com/01.06.21.1562.01









  


  








Input Form





Integrate[z^n E^(b z) Sin[c z] Sin[a z]^\[Nu], z] == ((-(I/2)) n! Sin[a z]^\[Nu] (E^((b + I c) z) Sum[(1/(n - p)!) ((-1)^p z^(n - p) (b + I c - I a \[Nu])^ (-1 - p) HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, 1 + p], -\[Nu]}, {1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, 1 + p]}, E^(2 I a z)]), {p, 0, n}] - E^((b - I c) z) Sum[(1/(n - p)!) ((-1)^p z^(n - p) (b - I c - I a \[Nu])^ (-1 - p) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, 1 + p], -\[Nu]}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, 1 + p]}, E^(2 I a z)]), {p, 0, n}]))/ (1 - E^(2 I a z))^\[Nu] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == ((-I) b + c - a \[Nu])/(2 a) && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == -((I b + c + a \[Nu])/(2 a)) && Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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Rule Form





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





2002-12-18