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 SinIntegral

 http://functions.wolfram.com/06.37.21.0052.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29