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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and a power functions > Involving cos and power > Involving zn cos(b zr) cosh(c z)





http://functions.wolfram.com/01.20.21.1036.01









  


  










Input Form





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










Standard Form





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MathML Form







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





2002-12-18