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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 zalpha-1eb zr+ecos(c zr+g)





http://functions.wolfram.com/01.07.21.0435.01









  


  








Input Form





Integrate[z^(2 n) E^(b z^2 + e) Cos[c z^2 + g], z] == (-(1/4)) z E^e ((E^(I g) (Erfc[Sqrt[(-b - I c) z^2]] Gamma[1/2 + n] + Sum[((-b - I c) z^2)^(1/2 + k)/Pochhammer[1/2 + n, 1 + k - n], {k, 0, -1 + n}]/E^((-b - I c) z^2) - Sum[((-b - I c) z^2)^(1/2 + k)/Pochhammer[1/2 + n, 1 + k - n], {k, n, -1}]/E^((-b - I c) z^2)))/(((-b - I c) z^2)^(1/2) (-b - I c)^n) + (Erfc[Sqrt[(-b + I c) z^2]] Gamma[1/2 + n] + Sum[((-b + I c) z^2)^(1/2 + k)/Pochhammer[1/2 + n, 1 + k - n], {k, 0, -1 + n}]/E^((-b + I c) z^2) - Sum[((-b + I c) z^2)^(1/2 + k)/Pochhammer[1/2 + n, 1 + k - n], {k, n, -1}]/E^((-b + I c) z^2))/(E^(I g) ((-b + I c) z^2)^(1/2) (-b + I c)^n)) /; Element[n, Integers]








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