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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric, exponential and a power functions > Involving powers of cos, exp and power > Involving zalpha-1ep zcosmu(c z+d)sinh(a z)





http://functions.wolfram.com/01.19.21.1430.01









  


  










Input Form





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





2002-12-18