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Sec






Mathematica Notation

Traditional Notation









Elementary Functions > Sec[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving cos and power > Involving zncos(a+b z)





http://functions.wolfram.com/01.11.21.0052.01









  


  










Input Form





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





2002-10-15





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