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 Cosh

 http://functions.wolfram.com/01.20.21.3808.01

 Input Form

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

 Standard Form

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 MathML Form

 p z cos ( b z ) cosh v ( c z 2 ) z 2 - v - 1 ( ( b + p ) z b + p + ( - b + p ) z - b + p ) ( 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) + 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]]]]] ( 1 ( 2 c k - c v ) ( c v - 2 c k ) ( - ( b + p ) 2 4 ( c v - 2 c k ) c v - 2 c k ( 2 c k - c v ) erfi ( b + p - 2 ( 2 c k - c v ) z 2 c v - 2 c k ) + - ( - b + p ) 2 4 ( 2 c k - c v ) ( c v - 2 c k ) 2 c k - c v erfi ( - b + p + 2 ( 2 c k - c v ) z 2 2 c k - c v ) ) + 1 ( 2 c k - c v ) ( c v - 2 c k ) ( - ( - b + p ) 2 4 ( c v - 2 c k ) c v - 2 c k ( 2 c k - c v ) erfi ( - b + p - 2 ( 2 c k - c v ) z 2 c v - 2 c k ) + - ( b + p ) 2 4 ( 2 c k - c v ) ( c v - 2 c k ) 2 c k - c v erfi ( b + p + 2 ( 2 c k - c v ) z 2 2 c k - c v ) ) ) /; v + Condition z p z b z c z 2 v 2 -1 v -1 b p z b p -1 -1 b p z -1 b p -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 1 2 k 0 v -1 2 -1 Binomial v k 1 2 c k -1 c v c v -1 2 c k -1 -1 b p 2 4 c v -1 2 c k -1 c v -1 2 c k 1 2 2 c k -1 c v Erfi b p -1 2 2 c k -1 c v z 2 c v -1 2 c k 1 2 -1 -1 -1 b p 2 4 2 c k -1 c v -1 c v -1 2 c k 2 c k -1 c v 1 2 Erfi -1 b p 2 2 c k -1 c v z 2 2 c k -1 c v 1 2 -1 1 2 c k -1 c v c v -1 2 c k -1 -1 -1 b p 2 4 c v -1 2 c k -1 c v -1 2 c k 1 2 2 c k -1 c v Erfi -1 b p -1 2 2 c k -1 c v z 2 c v -1 2 c k 1 2 -1 -1 b p 2 4 2 c k -1 c v -1 c v -1 2 c k 2 c k -1 c v 1 2 Erfi b p 2 2 c k -1 c v z 2 2 c k -1 c v 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18