Sine: Integration (formula 01.06.21.1469)

Sin

$Mathematica Notation$

Elementary Functions

Sin[z]

Integration

Indefinite integration

Involving functions of the direct function, exponential and a power functions

Involving powers of the direct function, exponential and a power functions

Involving powers of sin, exp and power

Involving z^alpha-1 e^{p z+e} sin^nu(a z+b)

http://functions.wolfram.com/01.06.21.1469.01

Input Form

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