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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 and a power functions > Involving cos and power > Involving zn cos(d z) sinh(c zr+g)





http://functions.wolfram.com/01.19.21.1065.01









  


  










Input Form





Integrate[z^n Cos[d z] Sinh[c z^2 + g], z] == (1/8) ((-c)^(-1 - n) E^(-(d^2/(4 c)) - g) Sum[2^(j - n) (I d)^(-j + n) ((-I) d - 2 c z)^(1 + j) (((-I) d - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, ((-I) d - 2 c z)^2/(4 c)], {j, 0, n}] + (-c)^(-1 - n) E^(-(d^2/(4 c)) - g) Sum[2^(j - n) ((-I) d)^(-j + n) (I d - 2 c z)^(1 + j) ((I d - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I d - 2 c z)^2/(4 c)], {j, 0, n}] - c^(-1 - n) E^(d^2/(4 c) + g) Sum[2^(j - n) (I d)^(-j + n) ((-I) d + 2 c z)^(1 + j) (-(((-I) d + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) d + 2 c z)^2/(4 c))], {j, 0, n}] - c^(-1 - n) E^(d^2/(4 c) + g) Sum[2^(j - n) ((-I) d)^(-j + n) (I d + 2 c z)^(1 + j) (-((I d + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I d + 2 c z)^2/(4 c))], {j, 0, n}]) /; Element[n, Integers] && n >= 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