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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving powers of the direct function and trigonometric functions > Involving powers of sin > Involving sinmu(c z)coshv(a z+b)





http://functions.wolfram.com/01.20.21.3133.01









  


  










Input Form





Integrate[Sin[c z]^m Cosh[b + a z]^\[Nu], z] == ((1/(a \[Nu])) Cosh[b + a z]^\[Nu] ((-Binomial[m, m/2]) Hypergeometric2F1[-(\[Nu]/2), -\[Nu], 1 - \[Nu]/2, -E^(-2 (b + a z))] (-1 + Mod[m, 2]) + I^(1 - m) a \[Nu] Sum[(-1)^k Binomial[m, k] ((E^(I c (-2 k + m) z) Hypergeometric2F1[ (I (2 c k - c m + I a \[Nu]))/(2 a), -\[Nu], (1/2) (2 - (I c (-2 k + m))/a - \[Nu]), -E^(-2 (b + a z))])/ (2 c k - c m + I a \[Nu]) - (E^(I (m Pi + 2 c k z - c m z)) Hypergeometric2F1[(I (c (-2 k + m) + I a \[Nu]))/(2 a), -\[Nu], (1/2) (2 - (I c (2 k - m))/a - \[Nu]), -E^(-2 (b + a z))])/ (2 c k - c m - I a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}]))/ (2^m (1 + E^(-2 (b + a z)))^\[Nu]) /; 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