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 CosIntegral

 http://functions.wolfram.com/06.38.21.0036.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29