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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving powers of the direct function and hyperbolic functions > Involving powers of sinh > Involving sinhmu(c z)coshv(a z)





http://functions.wolfram.com/01.20.21.4115.01









  


  








Input Form





Integrate[Sinh[c z]^m Cosh[a z]^\[Nu], z] == ((Binomial[m, m/2] Cosh[a z]^(1 + \[Nu]) Hypergeometric2F1[(1 + \[Nu])/2, 1/2, (3 + \[Nu])/2, Cosh[a z]^2] (-1 + Mod[m, 2]) (Sinh[a z]/(a (1 + \[Nu]) Sqrt[-Sinh[a z]^2])))/I^m + Sum[((-1)^(k + m) E^(c (2 k - m) z) Binomial[m, k] Cosh[a z]^\[Nu] (((-(-1)^m) E^(2 c (-2 k + m) z) (c (-2 k + m) + a \[Nu]) Hypergeometric2F1[-((2 c k - c m + a \[Nu])/(2 a)), -\[Nu], (1/2) (2 + (c (-2 k + m))/a - \[Nu]), -E^(2 a z)] + (c (-2 k + m) - a \[Nu]) Hypergeometric2F1[ -((c (-2 k + m) + a \[Nu])/(2 a)), -\[Nu], -((c (-2 k + m) + a (-2 + \[Nu]))/(2 a)), -E^(2 a z)])/ ((-c^2) (-2 k + m)^2 + a^2 \[Nu]^2)))/(1 + E^(2 a z))^\[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