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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and a power function > Involving products of powers of the direct function and a power function > Involving product of power of the direct function, the direct function and a power function > Involving zalpha-1cos(c z+d)cosv(a z+b)





http://functions.wolfram.com/01.07.21.1550.01









  


  










Input Form





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