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 CoshIntegral

 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

 z n sin ( b z ) Chi ( a z ) z - 4 ( b ) - n - 1 n ! ( - Ei ( - ( a + b ) z ) - ( - 1 ) n Ei ( ( a + b ) z ) - Ei ( ( a - b ) z ) - ( - 1 ) n Ei ( b z - a z ) + 4 Chi ( a z ) ( cos ( b z ) k = 0 n 2 ( ( b ) z ) 2 k + n - 2 n 2 ( 2 k + n - 2 n 2 ) ! - sin ( b z ) k = 0 n - 1 2 ( ( b ) z ) 2 k + n - 2 n - 1 2 - 1 ( 2 k + n - 2 n - 1 2 - 1 ) ! ) + ( a - b ) z k = 0 n m = k + 1 n ( b b - a ) m ( ( b - a ) k z k ) m k ! + ( - 1 ) n b z - 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 -1 b -1 n -1 n -1 ExpIntegralEi -1 a b z -1 -1 n ExpIntegralEi a b z -1 ExpIntegralEi a -1 b z -1 -1 n ExpIntegralEi b z -1 a z 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 b 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 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 z -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 a 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

© 1998-2013 Wolfram Research, Inc.