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 CosIntegral

 http://functions.wolfram.com/06.38.21.0062.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29