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 CoshIntegral

 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

 z n cosh ( b z ) Chi ( a z ) z 1 4 b - n - 1 n ! ( Ei ( ( - a - b ) z ) + Ei ( ( a - b ) z ) - ( - 1 ) n Ei ( ( b - a ) z ) - ( - 1 ) n Ei ( ( a + b ) z ) - 4 cosh ( b z ) Chi ( a z ) k = 0 n - 1 2 ( b z ) 2 k + n - 2 n - 1 2 - 1 ( 2 k + n - 2 n - 1 2 - 1 ) ! + 4 Chi ( a z ) sinh ( b z ) k = 0 n 2 ( b z ) 2 k + n - 2 n 2 ( 2 k + n - 2 n 2 ) ! - ( a - b ) z k = 0 n m = k + 1 n ( b b - a ) m ( ( b - a ) k z k ) m k ! + ( - 1 ) n ( b - a ) z k = 0 n m = k + 1 n ( b b - a ) m ( ( - 1 ) k ( b - a ) k z k ) m k ! - ( - a - b ) z k = 0 n m = k + 1 n ( b a + b ) m ( ( a + b ) k z k ) m k ! + ( - 1 ) n ( a + b ) z k = 0 n m = k + 1 n ( b a + b ) m ( ( - 1 ) k ( a + b ) k z k ) m k ! ) /; n Condition z z n b z CoshIntegral a z 1 4 b -1 n -1 n ExpIntegralEi -1 a -1 b z ExpIntegralEi a -1 b z -1 -1 n ExpIntegralEi b -1 a z -1 -1 n ExpIntegralEi a b z -1 4 b z CoshIntegral a z k 0 n -1 2 -1 b z 2 k n -1 2 n -1 2 -1 -1 2 k n -1 2 n -1 2 -1 -1 -1 4 CoshIntegral a z b z k 0 n 2 -1 b z 2 k n -1 2 n 2 -1 2 k n -1 2 n 2 -1 -1 -1 a -1 b z m k 1 n k 0 n b b -1 a -1 m b -1 a k z k m k -1 -1 n b -1 a z m k 1 n k 0 n b b -1 a -1 m -1 k b -1 a k z k m k -1 -1 -1 a -1 b z m k 1 n k 0 n b a b -1 m a b k z k m k -1 -1 n a b z m k 1 n k 0 n b a b -1 m -1 k a b k z k m k -1 n [/itex]

 Rule Form

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

 2001-10-29