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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric, exponential and a power functions > Involving powers of cos, exp and power > Involving zalpha-1ep zcosmu(c z)sinh(a z+b)





http://functions.wolfram.com/01.19.21.1431.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(p z) Cos[c z]^m Sinh[b + a z], z] == ((-2^(-1 - m)) z^\[Alpha] Binomial[m, m/2] ((E^(2 b) Gamma[\[Alpha], (-a - p) z])/((-a - p) z)^\[Alpha] - Gamma[\[Alpha], (a - p) z]/((a - p) z)^\[Alpha]) (1 - Mod[m, 2]))/E^b - (2^(-1 - m) z^\[Alpha] Sum[Binomial[m, s] ((-((a + I c m - p - 2 I c s) z)^(-\[Alpha])) Gamma[\[Alpha], (a + I c m - p - 2 I c s) z] + E^(2 b) (Gamma[\[Alpha], (-a + I c m - p - 2 I c s) z]/ ((-a + I c m - p - 2 I c s) z)^\[Alpha] + Gamma[\[Alpha], (-a - I c m - p + 2 I c s) z]/ ((-a - I c m - p + 2 I c s) z)^\[Alpha]) - Gamma[\[Alpha], (a - I c m - p + 2 I c s) z]/ ((a - I c m - p + 2 I c s) z)^\[Alpha]), {s, 0, Floor[(1/2) (-1 + m)]}])/E^b /; 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