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 CosIntegral

 http://functions.wolfram.com/06.38.21.0055.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29