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 Cosh

 http://functions.wolfram.com/01.20.21.1092.01

 Input Form

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

 Standard Form

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 MathML Form

 z n cos ( d z ) cosh ( c z 2 + f z + g ) z 1 8 ( - ( d - f ) 2 4 c - g ( j = 0 n 2 j - n ( f - d ) n - j ( - f + d - 2 c z ) j + 1 ( ( - f + 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 , ( - f + d - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 - ( - c ) - n - 1 ( - f - d ) 2 4 c - g j = 0 n 2 j - n ( f + d ) n - j ( - f - d - 2 c z ) j + 1 ( ( - f - 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 , ( - f - d - 2 c z ) 2 4 c ) - c - n - 1 - ( f - d ) 2 4 c + g j = 0 n 2 j - n ( d - f ) n - j ( f - d + 2 c z ) j + 1 ( - ( f - 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 , - ( f - d + 2 c z ) 2 4 c ) - c - n - 1 - ( f + d ) 2 4 c + g j = 0 n 2 j - n ( - f - d ) n - j ( f + d + 2 c z ) j + 1 ( - ( f + 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 , - ( f + d + 2 c z ) 2 4 c ) ) /; n Condition z z n d z c z 2 f z g 1 8 -1 d -1 f 2 4 c -1 -1 g j 0 n 2 j -1 n f -1 d n -1 j -1 f d -1 2 c z j 1 -1 f d -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f d -1 2 c z 2 4 c -1 -1 c -1 n -1 -1 -1 c -1 n -1 -1 f -1 d 2 4 c -1 -1 g j 0 n 2 j -1 n f d n -1 j -1 f -1 d -1 2 c z j 1 -1 f -1 d -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f -1 d -1 2 c z 2 4 c -1 -1 c -1 n -1 -1 f -1 d 2 4 c -1 g j 0 n 2 j -1 n d -1 f n -1 j f -1 d 2 c z j 1 -1 f -1 d 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f -1 d 2 c z 2 4 c -1 -1 c -1 n -1 -1 f d 2 4 c -1 g j 0 n 2 j -1 n -1 f -1 d n -1 j f d 2 c z j 1 -1 f d 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 f 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