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 Cosh

 http://functions.wolfram.com/01.20.21.0904.01

 Input Form

 Integrate[z^n Sin[d z + e] Cosh[c z^2], z] == (-(1/8)) I ((-c)^(-1 - n) E^(-(d^2/(4 c)) - I e) Sum[2^(j - n) (I d)^(-j + n) ((-I) d - 2 c z)^(1 + j) (((-I) d - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, ((-I) d - 2 c z)^2/(4 c)], {j, 0, n}] - (-c)^(-1 - n) E^(-(d^2/(4 c)) + I e) Sum[2^(j - n) ((-I) d)^(-j + n) (I d - 2 c z)^(1 + j) ((I d - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I d - 2 c z)^2/(4 c)], {j, 0, n}] + c^(-1 - n) E^(d^2/(4 c) - I e) Sum[2^(j - n) (I d)^(-j + n) ((-I) d + 2 c z)^(1 + j) (-(((-I) d + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) d + 2 c z)^2/(4 c))], {j, 0, n}] - c^(-1 - n) E^(d^2/(4 c) + I e) Sum[2^(j - n) ((-I) d)^(-j + n) (I d + 2 c z)^(1 + j) (-((I d + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I d + 2 c z)^2/(4 c))], {j, 0, n}]) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n sin ( e + d z ) cosh ( c z 2 ) z - 1 8 ( - d 2 4 c - e ( j = 0 n 2 j - n ( d ) n - j ( - d - 2 c z ) j + 1 ( ( - d - 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( - d - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 - - d 2 4 c + e ( j = 0 n 2 j - n ( - d ) n - j ( d - 2 c z ) j + 1 ( ( d - 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , ( d - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 + c - n - 1 d 2 4 c - e j = 0 n 2 j - n ( d ) n - j ( - d + 2 c z ) j + 1 ( - ( - d + 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( - d + 2 c z ) 2 4 c ) - c - n - 1 d 2 4 c + e j = 0 n 2 j - n ( - d ) n - j ( d + 2 c z ) j + 1 ( - ( d + 2 c z ) 2 c ) 1 2 ( - j - 1 ) ( n j ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["j", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( j + 1 2 , - ( d + 2 c z ) 2 4 c ) ) /; n Condition z z n e d z c z 2 -1 1 8 -1 d 2 4 c -1 -1 e j 0 n 2 j -1 n d n -1 j -1 d -1 2 c z j 1 -1 d -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d -1 2 c z 2 4 c -1 -1 c -1 n -1 -1 -1 d 2 4 c -1 e j 0 n 2 j -1 n -1 d n -1 j d -1 2 c z j 1 d -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 d -1 2 c z 2 4 c -1 -1 c -1 n -1 c -1 n -1 d 2 4 c -1 -1 e j 0 n 2 j -1 n d n -1 j -1 d 2 c z j 1 -1 -1 d 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 d 2 c z 2 4 c -1 -1 c -1 n -1 d 2 4 c -1 e j 0 n 2 j -1 n -1 d n -1 j d 2 c z j 1 -1 d 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 d 2 c z 2 4 c -1 n [/itex]

 Rule Form

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

 2002-12-18