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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0054.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29