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 SinIntegral

 http://functions.wolfram.com/06.37.21.0040.01

 Input Form

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

 Standard Form

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 MathML Form

 z n cosh ( b z ) Si ( a z ) z - 4 b - n - 1 n ! ( ( - 1 ) n Ei ( ( b - a ) z ) - ( - 1 ) - n Ei ( ( b + a ) z ) - Ei ( - b z + a ( - ) z ) + Ei ( a z - b z ) + 1 Γ ( n + 2 ) ( 2 ( n + 1 ) ( ( - 1 ) n Γ ( n + 1 , - b z ) - Γ ( n + 1 , b z ) ) Si ( a z ) ) - ( - 1 ) n ( b - a ) z m = 1 n 1 m ( b b - a ) m k = 0 m - 1 ( a - b ) k 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 ! + - ( b + a ) z m = 1 n 1 m ( b b + a ) m k = 0 m - 1 ( b + a ) k z k k ! - a z - b 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 SinIntegral a z -1 4 -1 b -1 n -1 n -1 n ExpIntegralEi b -1 a z -1 -1 -1 n ExpIntegralEi b a z -1 ExpIntegralEi -1 b z a -1 z ExpIntegralEi a z -1 b z 1 Gamma n 2 -1 2 n 1 -1 n Gamma n 1 -1 b z -1 Gamma n 1 b z SinIntegral a z -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 -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 b a z m 1 n 1 m -1 b b a -1 m k 0 m -1 b a k z k k -1 -1 a z -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 n [/itex]

 Rule Form

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

 2001-10-29

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