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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of powers of two direct functions > Involving sinmu(c z+d)sinv(a z+b)





http://functions.wolfram.com/01.06.21.0787.01









  


  








Input Form





Integrate[Sin[d + c z]^\[Mu] Sin[b + a z]^v, z] == ((I/(c \[Mu])) Sin[d + c z]^\[Mu] (Binomial[v, v/2] Hypergeometric2F1[-(\[Mu]/2), -\[Mu], 1 - \[Mu]/2, E^(2 I (d + c z))] (1 - Mod[v, 2]) + (c \[Mu] Sum[(-1)^k E^(I b (-2 k + v)) Binomial[v, k] ((E^(I a (-2 k + v) z) Hypergeometric2F1[-((2 a k - a v + c \[Mu])/( 2 c)), -\[Mu], (1/2) (2 + (a (-2 k + v))/c - \[Mu]), E^(2 I (d + c z))])/(2 a k - a v + c \[Mu]) + (E^(I (4 b k - 2 b v + Pi v + 2 a k z - a v z)) Hypergeometric2F1[ -((-2 a k + a v + c \[Mu])/(2 c)), -\[Mu], (1/2) (2 + (a (2 k - v))/c - \[Mu]), E^(2 I (d + c z))])/ (-2 a k + a v + c \[Mu])), {k, 0, Floor[(1/2) (-1 + v)]}])/I^v))/ (2^v (1 - E^(2 I (d + c z)))^\[Mu]) /; Element[v, Integers] && v > 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