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Sin




Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function, exponential and a power functions > Involving powers of the direct function, exponential and a power functions > Involving powers of sin, exp and power > Involving zn eb zrsinv(c z)





http://functions.wolfram.com/01.06.21.1475.01









  


  








Input Form





Integrate[z^n E^(b z^2) Sin[c z]^v, z] == (-2^(-1 - v)) z^(1 + n) ((-b) z^2)^((1/2) (-1 - n)) Binomial[v, v/2] Gamma[(1 + n)/2, (-b) z^2] (1 - Mod[v, 2]) - (2^(-1 - v) b^(-1 - n) Sum[(-1)^k E^((c^2 (-2 k + v)^2)/(4 b)) Binomial[v, k] ((-1)^v Sum[2^(-n + q) (I c (-2 k + v))^(n - q) (2 I c k - I c v + 2 b z)^(1 + q) (-((2 I c k - I c v + 2 b z)^2/ b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((2 I c k - I c v + 2 b z)^2/(4 b))], {q, 0, n}] + Sum[(I c (k - v/2))^(n - q) (I c (-2 k + v) + 2 b z)^(1 + q) (-((I c (-2 k + v) + 2 b z)^2/b))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((I c (-2 k + v) + 2 b z)^2/(4 b))], {q, 0, n}]), {k, 0, Floor[(1/2) (-1 + v)]}])/I^v /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0








Standard Form





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MathML Form







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<annotation-xml encoding='MathML-Content'> <apply> <rem /> <ci> $CellContext`v </ci> <cn type='integer'> 2 </cn> </apply> </annotation-xml> </semantics> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8469; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> v </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <ci> n </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <ci> v </ci> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> 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</apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </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> q </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <apply> <plus /> <ci> q </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 /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b 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Rule Form





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





2002-12-18