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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zn eb zr cos(f z+g)





http://functions.wolfram.com/01.07.21.0338.01









  


  








Input Form





Integrate[z^n E^(b z^2) Cos[f z + g], z] == (-(1/4)) b^(-1 - n) (E^(f^2/(4 b) - I g) Sum[2^(-n + q) (I f)^(n - q) ((-I) f + 2 b z)^(1 + q) (-(((-I) f + 2 b z)^2/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -(((-I) f + 2 b z)^2/(4 b))], {q, 0, n}] + E^(f^2/(4 b) + I g) Sum[2^(-n + q) ((-I) f)^(n - q) (I f + 2 b z)^(1 + q) (-((I f + 2 b z)^2/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I f + 2 b z)^2/(4 b))], {q, 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