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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0078.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29