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 Cosh

 http://functions.wolfram.com/01.20.21.1291.01

 Input Form

 Integrate[E^(p z^2) Cos[b z]^m Cosh[c z], z] == (1/Sqrt[p]) ((2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Erfi[(-c + 2 p z)/(2 Sqrt[p])] + Erfi[(c + 2 p z)/(2 Sqrt[p])]) (1 - Mod[m, 2]))/E^(c^2/(4 p))) + (1/Sqrt[p]) (2^(-2 - m) Sqrt[Pi] Sum[Binomial[m, s] (Erfi[(-c + I b m - 2 I b s + 2 p z)/(2 Sqrt[p])]/ E^((-c + I b m - 2 I b s)^2/(4 p)) + Erfi[(c + I b m - 2 I b s + 2 p z)/(2 Sqrt[p])]/ E^((c + I b m - 2 I b s)^2/(4 p)) + Erfi[(-c - I b m + 2 I b s + 2 p z)/(2 Sqrt[p])]/ E^((-c - I b m + 2 I b s)^2/(4 p)) + Erfi[(c - I b m + 2 I b s + 2 p z)/(2 Sqrt[p])]/ E^((c - I b m + 2 I b s)^2/(4 p))), {s, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 p z 2 cos m ( b z ) cosh ( c z ) z 2 - m - 2 - c 2 4 p π ( m m 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox[FractionBox["m", "2"], Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( erfi ( 2 p z - c 2 p ) + erfi ( c + 2 p z 2 p ) ) ( 1 - m mod 2 \$CellContext`m 2 ) p + 1 p ( 2 - m - 2 π s = 0 m - 1 2 ( m s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["m", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( - ( - c - b m + 2 b s ) 2 4 p erfi ( - c - b m + 2 b s + 2 p z 2 p ) + - ( c - b m + 2 b s ) 2 4 p erfi ( c - b m + 2 b s + 2 p z 2 p ) + - ( - c + b m - 2 b s ) 2 4 p erfi ( - c + b m - 2 b s + 2 p z 2 p ) + - ( c + b m - 2 b s ) 2 4 p erfi ( c + b m - 2 b s + 2 p z 2 p ) ) ) /; m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m > 0 Condition z p z 2 b z m c z 2 -1 m -2 -1 c 2 4 p -1 1 2 Binomial m m 2 -1 Erfi 2 p z -1 c 2 p 1 2 -1 Erfi c 2 p z 2 p 1 2 -1 1 -1 \$CellContext`m 2 p 1 2 -1 1 p 1 2 -1 2 -1 m -2 1 2 s 0 m -1 2 -1 Binomial m s -1 -1 c -1 b m 2 b s 2 4 p -1 Erfi -1 c -1 b m 2 b s 2 p z 2 p 1 2 -1 -1 c -1 b m 2 b s 2 4 p -1 Erfi c -1 b m 2 b s 2 p z 2 p 1 2 -1 -1 -1 c b m -1 2 b s 2 4 p -1 Erfi -1 c b m -1 2 b s 2 p z 2 p 1 2 -1 -1 c b m -1 2 b s 2 4 p -1 Erfi c b m -1 2 b s 2 p z 2 p 1 2 -1 m m 0 [/itex]

 Rule Form

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

 2002-12-18