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Sech




Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving functions of the direct function, hyperbolic and exponential functions > Involving powers of the direct function, hyperbolic and exponential functions > Involving powers of sinh and exp > Involving ep z sinhu(b z) sechnu(c z)





http://functions.wolfram.com/01.24.21.0495.01









  


  








Input Form





Integrate[E^(p z) Sinh[b z]^u Sech[c z]^\[Nu], z] == -((1/(p + c \[Nu])) ((I/2)^u E^(p z) (1 + E^(2 c z))^\[Nu] Binomial[u, u/2] HypergeometricPFQ[{p/(2 c) + \[Nu]/2, \[Nu]}, {1 + p/(2 c) + \[Nu]/2}, -E^(2 c z)] (-1 + Mod[u, 2]) Sech[c z]^\[Nu])) + (I^u (1 + E^(2 c z))^\[Nu] Sech[c z]^\[Nu] Sum[(-1)^k Binomial[u, k] ((E^((I Pi u)/2 + (p - b (-2 k + u)) z) HypergeometricPFQ[{(b k)/c + p/(2 c) - (b u)/(2 c) + \[Nu]/2, \[Nu]}, {1 + (b k)/c + p/(2 c) - (b u)/(2 c) + \[Nu]/2}, -E^(2 c z)])/(p - b (-2 k + u) + c \[Nu]) + (E^((-(1/2)) I Pi u + (p + b (-2 k + u)) z) HypergeometricPFQ[ {-((b k)/c) + p/(2 c) + (b u)/(2 c) + \[Nu]/2, \[Nu]}, {1 - (b k)/c + p/(2 c) + (b u)/(2 c) + \[Nu]/2}, -E^(2 c z)])/ (p + b (-2 k + u) + c \[Nu])), {k, 0, Floor[(1/2) (-1 + u)]}])/ 2^u /; Element[u, Integers] && u > 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