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 SinIntegral

 http://functions.wolfram.com/06.37.21.0041.01

 Input Form

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

 Standard Form

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 MathML Form

 z n cosh ( a z ) Chi ( a z ) z ( - 1 ) n 4 a - n - 1 ( 2 Chi ( a z ) ( Γ ( n + 1 , - a z ) - ( - 1 ) n Γ ( n + 1 , a z ) ) + n ! ( ( - 1 ) n Ei ( - 2 a z ) - Ei ( 2 a z ) + ( ( - 1 ) n - 1 ) log ( z ) - 2 k = 1 n ( - a ) k k ! ( z k 2 k - 2 - k - 1 ( - a ) - k Γ ( k , - 2 a z ) ) + 2 ( - 1 ) n k = 1 n a k k ! ( z k 2 k - 2 - k - 1 a - k Γ ( k , 2 a z ) ) ) ) /; n Condition z z n a z CoshIntegral a z -1 n 4 -1 a -1 n -1 2 CoshIntegral a z Gamma n 1 -1 a z -1 -1 n Gamma n 1 a z n -1 n ExpIntegralEi -2 a z -1 ExpIntegralEi 2 a z -1 n -1 z -1 2 k 1 n -1 a k k -1 z k 2 k -1 -1 2 -1 k -1 -1 a -1 k Gamma k -2 a z 2 -1 n k 1 n a k k -1 z k 2 k -1 -1 2 -1 k -1 a -1 k Gamma k 2 a z n [/itex]

 Rule Form

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

 2001-10-29