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 CosIntegral

 http://functions.wolfram.com/06.38.21.0066.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29