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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and a power functions > Involving powers of the direct function, hyperbolic and a power functions > Involving sinh and power > Involving zalpha-1sinh(c z+d)coshv(a z+b)





http://functions.wolfram.com/01.20.21.4450.01









  


  










Input Form





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