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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and trigonometric functions > Involving powers of the direct function, hyperbolic and trigonometric functions > Involving powers of sin and powers of coth > Involving sinm(a z) cothmu(c z) sechnu(c z)





http://functions.wolfram.com/01.24.21.0538.01









  


  










Input Form





Integrate[Sin[a z]^m Coth[c z]^\[Mu] Sech[c z]^\[Nu], z] == -((1/(c \[Nu])) (((1 - E^(-2 c z))^\[Mu] (1 + E^(-2 c z))^(-\[Mu] + \[Nu]) AppellF1[\[Nu]/2, -\[Mu] + \[Nu], \[Mu], (2 + \[Nu])/2, -E^(-2 c z), E^(-2 c z)] Binomial[m, m/2] Coth[c z]^\[Mu] (1 - Mod[m, 2]) Sech[c z]^\[Nu])/2^m)) + ((1 - E^(-2 c z))^\[Mu] (1 + E^(-2 c z))^(-\[Mu] + \[Nu]) Coth[c z]^\[Mu] Sech[c z]^\[Nu] Sum[(-1)^k Binomial[m, k] ((E^((I m Pi)/2 - I a (-2 k + m) z) AppellF1[-(((-I) a (-2 k + m) - c \[Nu])/(2 c)), -\[Mu] + \[Nu], \[Mu], (1/2) (2 + (I a (-2 k + m))/c + \[Nu]), -E^(-2 c z), E^(-2 c z)])/((-I) a (-2 k + m) - c \[Nu]) + (E^((-(1/2)) I m Pi + I a (-2 k + m) z) AppellF1[ -((I a (-2 k + m) - c \[Nu])/(2 c)), -\[Mu] + \[Nu], \[Mu], (1/2) (2 - (I a (-2 k + m))/c + \[Nu]), -E^(-2 c z), E^(-2 c z)])/ (I a (-2 k + m) - c \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}])/2^m /; Element[m, Integers] && m > 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