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 Cosh

 http://functions.wolfram.com/01.20.21.1052.01

 Input Form

 Integrate[z^n Cos[b z] Cosh[c z^2], z] == (1/8) (((-(-c)^(-1 - n)) Sum[2^(j - n) (I b)^(-j + n) ((-I) b - 2 c z)^(1 + j) (((-I) b - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, ((-I) b - 2 c z)^2/(4 c)], {j, 0, n}])/E^(b^2/(4 c)) - ((-c)^(-1 - n) Sum[2^(j - n) ((-I) b)^(-j + n) (I b - 2 c z)^(1 + j) ((I b - 2 c z)^2/c)^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, (I b - 2 c z)^2/(4 c)], {j, 0, n}])/E^(b^2/(4 c)) - c^(-1 - n) E^(b^2/(4 c)) Sum[2^(j - n) (I b)^(-j + n) ((-I) b + 2 c z)^(1 + j) (-(((-I) b + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -(((-I) b + 2 c z)^2/(4 c))], {j, 0, n}] - c^(-1 - n) E^(b^2/(4 c)) Sum[2^(j - n) ((-I) b)^(-j + n) (I b + 2 c z)^(1 + j) (-((I b + 2 c z)^2/c))^((1/2) (-1 - j)) Binomial[n, j] Gamma[(1 + j)/2, -((I b + 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 ( b z ) cosh ( c z 2 ) z 1 8 ( - - b 2 4 c ( j = 0 n 2 j - n ( - b ) n - j ( b - 2 c z ) j + 1 ( ( b - 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 , ( b - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 - ( - c ) - n - 1 - b 2 4 c j = 0 n 2 j - n ( b ) n - j ( - b - 2 c z ) j + 1 ( ( - b - 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 , ( - b - 2 c z ) 2 4 c ) - c - n - 1 b 2 4 c j = 0 n 2 j - n ( b ) n - j ( - b + 2 c z ) j + 1 ( - ( - b + 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 , - ( - b + 2 c z ) 2 4 c ) - c - n - 1 b 2 4 c j = 0 n 2 j - n ( - b ) n - j ( b + 2 c z ) j + 1 ( - ( b + 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 , - ( b + 2 c z ) 2 4 c ) ) /; n Condition z z n b z c z 2 1 8 -1 -1 b 2 4 c -1 j 0 n 2 j -1 n -1 b n -1 j b -1 2 c z j 1 b -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 b -1 2 c z 2 4 c -1 -1 c -1 n -1 -1 -1 c -1 n -1 -1 b 2 4 c -1 j 0 n 2 j -1 n b n -1 j -1 b -1 2 c z j 1 -1 b -1 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 b -1 2 c z 2 4 c -1 -1 c -1 n -1 b 2 4 c -1 j 0 n 2 j -1 n b n -1 j -1 b 2 c z j 1 -1 -1 b 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 -1 b 2 c z 2 4 c -1 -1 c -1 n -1 b 2 4 c -1 j 0 n 2 j -1 n -1 b n -1 j b 2 c z j 1 -1 b 2 c z 2 c -1 1 2 -1 j -1 Binomial n j Gamma j 1 2 -1 -1 b 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