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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 coth, exp and power > Involving zn ep zcoth(c z) sech( c z)





http://functions.wolfram.com/01.24.21.0243.01









  


  










Input Form





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