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 SinIntegral

 http://functions.wolfram.com/06.37.21.0056.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29