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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and a power functions > Involving powers of the direct function, trigonometric and a power functions > Involving sin and power > Involving zalpha-1sin(c z)cosv(a z+b)





http://functions.wolfram.com/01.07.21.2425.01









  


  










Input Form





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










Standard Form





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MathML Form







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</mo> <mi> a </mi> <mo> &#8290; </mo> <mi> s </mi> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> v </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> v </mi> <mo> &#8712; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </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> <apply> <plus /> <ci> &#945; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <cos /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> <ci> v </ci> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> v </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#945; 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Rule Form





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





2002-12-18