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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic, exponential and a power functions > Involving cosh, exp and power > Involving zn ep zcosh(b z) sech( c z)





http://functions.wolfram.com/01.24.21.0230.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> </apply> <apply> <neq /> <apply> <plus /> <ci> b </ci> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <neq /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18