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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric, exponential and a power functions > Involving powers of the direct function, trigonometric, exponential and a power functions > Involving cos, exp and power > Involving zalpha-1ep zcos(c z+d)coshnu(a z)





http://functions.wolfram.com/01.20.21.3967.01









  


  










Input Form





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