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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and a power functions > Involving sinh and power > Involving zn sinh(b zr+d z) cosh(c z)





http://functions.wolfram.com/01.20.21.1667.01









  


  










Input Form





Integrate[z^n Sinh[b z^2 + d z] Cosh[c z], z] == ((-b)^(-1 - n)/8) (E^((c + d)^2/(4 b)) Sum[(Binomial[n, q] 2^(q - n) (c + d)^(n - q) (-c - d - 2 b z)^(1 + q) Gamma[(1 + q)/2, (-c - d - 2 b z)^2/(4 b)])/((-c - d - 2 b z)^2/b)^ ((1/2) (q + 1)), {q, 0, n}] + E^((c - d)^2/(4 b)) Sum[(Binomial[n, q] 2^(q - n) (d - c)^(n - q) (c - d - 2 b z)^(1 + q) Gamma[(1 + q)/2, (c - d - 2 b z)^2/(4 b)])/((c - d - 2 b z)^2/b)^ ((1/2) (q + 1)), {q, 0, n}]) - (b^(-1 - n)/8) (Sum[(Binomial[n, q] 2^(q - n) (c - d)^(n - q) (d - c + 2 b z)^(1 + q) Gamma[(1 + q)/2, -((d - c + 2 b z)^2/(4 b))])/ (-((d - c + 2 b z)^2/b))^((1/2) (q + 1)), {q, 0, n}]/ E^((c - d)^2/(4 b)) + Sum[(Binomial[n, q] 2^(q - n) (-(c + d))^(n - q) ((c + d) + 2 b z)^(1 + q) Gamma[(1 + q)/2, -((c + d + 2 b z)^2/(4 b))])/(-((c + d + 2 b z)^2/b))^ ((1/2) (q + 1)), {q, 0, n}]/E^((c + d)^2/(4 b))) /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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<mi> d </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mi> d </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mi> b </mi> </mfrac> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> q </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> + </mo> <mi> d </mi> <mo> + 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Date Added to functions.wolfram.com (modification date)





2002-12-18