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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 sin, exp and power > Involving zalpha-1ep zsinmu(c z+d)sinh(a z+b)





http://functions.wolfram.com/01.19.21.1381.01









  


  










Input Form





Integrate[z^(\[Alpha] - 1) E^(p z) Sin[d + 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[(-1)^k E^(-b - 2 I d k - I d m - (I m Pi)/2) Binomial[m, k] (((-E^(2 I d m + I Pi)) Gamma[\[Alpha], (a + 2 I c k - I c m - p) z])/((a + 2 I c k - I c m - p) z)^ \[Alpha] + E^(2 b) (((-E^(2 I d m)) Gamma[\[Alpha], (-a + 2 I c k - I c m - p) z])/((-a + 2 I c k - I c m - p) z)^ \[Alpha] - (E^(4 I d k + I m Pi) Gamma[\[Alpha], (-a - 2 I c k + I c m - p) z])/((-a - 2 I c k + I c m - p) z)^ \[Alpha]) - (E^(4 I d k + I Pi + I m Pi) Gamma[\[Alpha], (a - 2 I c k + I c m - p) z])/((a - 2 I c k + I c m - p) z)^ \[Alpha]), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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Date Added to functions.wolfram.com (modification date)





2002-12-18