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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and power factors > Involving power > Involving zn cos(a zr+b z)





http://functions.wolfram.com/01.07.21.0511.01









  


  








Input Form





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








Standard Form





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MathML Form







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<times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <plus /> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> j </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Binomial </ci> <ci> n </ci> <ci> j </ci> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> j </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18