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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 tanh and exp > Involving ep ztanh(c z) sechv( c z)





http://functions.wolfram.com/01.24.21.0505.01









  


  










Input Form





Integrate[E^(p z) Tanh[c z] Sech[c z]^\[Nu], z] == E^((-2 c + p) z) (1 + E^(-2 c z))^\[Nu] Sech[c z]^\[Nu] ((-(p - c \[Nu] + E^(2 c z) (-p + c (2 + \[Nu])))) (HypergeometricPFQ[{-(p/(2 c)) + \[Nu]/2, 1 + \[Nu]}, {2 - p/(2 c) + \[Nu]/2}, -E^(-2 c z)]/((p - c \[Nu]) (p - c (2 + \[Nu])))) + 2 c (1 - E^(-2 c z)) (1 + \[Nu]) (HypergeometricPFQ[{1 - p/(2 c) + \[Nu]/2, 2 + \[Nu]}, {3 - p/(2 c) + \[Nu]/2}, -E^(-2 c z)]/((-p + c (2 + \[Nu])) (-p + c (4 + \[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