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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 hyperbolic functions and a power function > Involving cosh and power





http://functions.wolfram.com/06.40.21.0038.01









  


  










Input Form





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










Standard Form





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MathML Form







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Rule Form





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





2001-10-29





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