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 Cosh

 http://functions.wolfram.com/01.20.21.3802.01

 Input Form

 Integrate[E^(p z^2) Cos[b z^2] Cosh[c z]^v, z] == (1/(b^2 + p^2)) (2^(-2 - v) Sqrt[Pi] (Binomial[v, v/2] (Sqrt[(-I) b + p] (I b + p) Erfi[Sqrt[(-I) b + p] z] + ((-I) b + p) Sqrt[I b + p] Erfi[Sqrt[I b + p] z]) (1 - Mod[v, 2]) + Sum[Binomial[v, s] (E^((c^2 (-2 s + v)^2)/(4 (I b - p))) Sqrt[(-I) b + p] (I b + p) (Erfi[(2 c s - c v - 2 I b z + 2 p z)/ (2 Sqrt[(-I) b + p])] + Erfi[(c (-2 s + v) + 2 ((-I) b + p) z)/ (2 Sqrt[(-I) b + p])]) - ((I b - p) Sqrt[I b + p] (Erfi[(c (2 s - v) + 2 (I b + p) z)/(2 Sqrt[I b + p])] + Erfi[(c (-2 s + v) + 2 (I b + p) z)/(2 Sqrt[I b + p])]))/ E^((c^2 (-2 s + v)^2)/(4 (I b + p)))), {s, 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 2 ) cosh v ( c z ) z 2 - v - 2 π b 2 + p 2 ( ( 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]]]]] ( - b + p ( b + p ) erfi ( - b + p z ) + ( - b + p ) b + p erfi ( b + p z ) ) ( 1 - v mod 2 \$CellContext`v 2 ) + s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( c 2 ( v - 2 s ) 2 4 ( b - p ) - b + p ( b + p ) ( erfi ( 2 c s - c v - 2 b z + 2 p z 2 - b + p ) + erfi ( c ( v - 2 s ) + 2 ( - b + p ) z 2 - b + p ) ) - - c 2 ( v - 2 s ) 2 4 ( b + p ) ( b - p ) b + p ( erfi ( c ( 2 s - v ) + 2 ( b + p ) z 2 b + p ) + erfi ( c ( v - 2 s ) + 2 ( b + p ) z 2 b + p ) ) ) ) /; v + Condition z p z 2 b z 2 c z v 2 -1 v -2 1 2 b 2 p 2 -1 Binomial v v 2 -1 -1 b p 1 2 b p Erfi -1 b p 1 2 z -1 b p b p 1 2 Erfi b p 1 2 z 1 -1 \$CellContext`v 2 s 0 v -1 2 -1 Binomial v s c 2 v -1 2 s 2 4 b -1 p -1 -1 b p 1 2 b p Erfi 2 c s -1 c v -1 2 b z 2 p z 2 -1 b p 1 2 -1 Erfi c v -1 2 s 2 -1 b p z 2 -1 b p 1 2 -1 -1 -1 c 2 v -1 2 s 2 4 b p -1 b -1 p b p 1 2 Erfi c 2 s -1 v 2 b p z 2 b p 1 2 -1 Erfi c v -1 2 s 2 b p z 2 b p 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18