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 Cosh

 http://functions.wolfram.com/01.20.21.0372.01

 Input Form

 Integrate[z^n E^(b z) Cosh[c z^2], z] == (-(1/4)) ((-c)^(-1 - n) E^(b^2/(4 c)) Sum[2^(-n + q) (-b)^(n - q) (b - 2 c z)^(1 + q) ((b - 2 c z)^2/c)^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, (b - 2 c z)^2/(4 c)], {q, 0, n}] + (c^(-1 - n) Sum[2^(-n + q) (-b)^(n - q) (b + 2 c z)^(1 + q) (-((b + 2 c z)^2/c))^((1/2) (-1 - q)) Binomial[n, q] Gamma[(1 + q)/2, -((b + 2 c z)^2/(4 c))], {q, 0, n}])/ E^(b^2/(4 c))) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n b z cosh ( c z 2 ) z - 1 4 ( b 2 4 c ( q = 0 n 2 q - n ( - b ) n - q ( b - 2 c z ) q + 1 ( ( b - 2 c z ) 2 c ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , ( b - 2 c z ) 2 4 c ) ) ( - c ) - n - 1 + c - n - 1 - b 2 4 c q = 0 n 2 q - n ( - b ) n - q ( b + 2 c z ) q + 1 ( - ( b + 2 c z ) 2 c ) 1 2 ( - q - 1 ) ( n q ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", Identity]], List[TagBox["q", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] Γ ( q + 1 2 , - ( b + 2 c z ) 2 4 c ) ) /; n Condition z z n b z c z 2 -1 1 4 b 2 4 c -1 q 0 n 2 q -1 n -1 b n -1 q b -1 2 c z q 1 b -1 2 c z 2 c -1 1 2 -1 q -1 Binomial n q Gamma q 1 2 -1 b -1 2 c z 2 4 c -1 -1 c -1 n -1 c -1 n -1 -1 b 2 4 c -1 q 0 n 2 q -1 n -1 b n -1 q b 2 c z q 1 -1 b 2 c z 2 c -1 1 2 -1 q -1 Binomial n q Gamma q 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