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 SinIntegral

 http://functions.wolfram.com/06.37.21.0014.01

 Input Form

 Integrate[z^n E^(b z) SinIntegral[a z], z] == (n!/2) (-b)^(-n - 1) (-2 SinIntegral[a z] E^(b z) Sum[((-b) z)^k/k!, {k, 0, n}] + I ExpIntegralEi[((-I) a + b) z] - I ExpIntegralEi[(I a + b) z] + I 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}] - I 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 b z Si ( a z ) z 1 2 n ! ( - b ) - n - 1 ( Ei ( ( b - a ) z ) - Ei ( ( b + a ) z ) - 2 b z Si ( a z ) k = 0 n ( - b 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 ! - ( b - a ) z m = 1 n 1 m ( b b - a ) m k = 0 m - 1 ( a - b ) k z k k ! ) z z n b z SinIntegral a z 1 2 n -1 b -1 n -1 ExpIntegralEi b -1 a z -1 ExpIntegralEi b a z -1 2 b z SinIntegral a z k 0 n -1 b z k k -1 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 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 [/itex]

 Rule Form

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

 2001-10-29