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 Cosh

 http://functions.wolfram.com/01.20.21.3804.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18