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CoshIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CoshIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving sin and power





http://functions.wolfram.com/06.40.21.0022.01









  


  










Input Form





Integrate[z^n Sin[b z] CoshIntegral[a z], z] == (-(I/4)) (I b)^(-1 - n) n! (-ExpIntegralEi[(a - I b) z] - ExpIntegralEi[(-(a + I b)) z] - (-1)^n ExpIntegralEi[(a + I b) z] - (-1)^n ExpIntegralEi[(-a) z + I b z] + 4 CoshIntegral[a z] ((-I) Sin[b z] Sum[((I b) z)^(2 k + n - 2 Floor[(n - 1)/2] - 1)/ (2 k + n - 2 Floor[(n - 1)/2] - 1)!, {k, 0, Floor[(n - 1)/2]}] + Cos[b z] Sum[((I b) z)^(2 k + n - 2 Floor[n/2])/ (2 k + n - 2 Floor[n/2])!, {k, 0, Floor[n/2]}]) + E^((a - I b) z) Sum[(((I b)/(I b - a))^m ((I b - a)^k z^k))/(m k!), {k, 0, n}, {m, k + 1, n}] + (-1)^n E^((-a) z + I b z) Sum[(((I b)/(I b - a))^m ((-1)^k (I b - a)^k z^k))/(m k!), {k, 0, n}, {m, k + 1, n}] + Sum[(((I b)/(I b + a))^m ((a + I b)^k z^k))/(m k!), {k, 0, n}, {m, k + 1, n}]/E^((a + I b) z) + (-1)^n E^((a + I b) z) Sum[(((I b)/(I b + a))^m ((-1)^k (a + I b)^k z^k))/(m k!), {k, 0, n}, {m, k + 1, n}]) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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k </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mi> k </mi> <mo> ! </mo> </mrow> </mrow> </mfrac> </mrow> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> m </mi> <mo> = </mo> <mrow> <mi> k </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mi> n </mi> </munderover> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </mrow> </mfrac> <mo> ) </mo> 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Date Added to functions.wolfram.com (modification date)





2001-10-29





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