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 Cosh

 http://functions.wolfram.com/01.20.21.0386.01

 Input Form

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

 Standard Form

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 MathML Form

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