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Csch






Mathematica Notation

Traditional Notation









Elementary Functions > Csch[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and a power functions > Involving powers of the direct function, trigonometric and a power functions > Involving sin and power > Involving znsin(a+b z) cschv( c z)





http://functions.wolfram.com/01.23.21.0351.01









  


  










Input Form





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










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