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 Cosh

 http://functions.wolfram.com/01.20.21.1297.01

 Input Form

 Integrate[E^(p z^2) Cos[b z]^m Cosh[c z^2], z] == (1/((-c + p) (c + p))) (2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] ((-c + p) Sqrt[c + p] Erfi[Sqrt[c + p] z] + Sqrt[-c + p] (c + p) Erfi[(-2 c z + 2 p z)/(2 Sqrt[-c + p])]) (1 - Mod[m, 2])) + ((2^(-2 - m) Sqrt[Pi])/((-c + p) (c + p))) Sum[Binomial[m, s] (((-c + p) Sqrt[c + p] Erfi[((-I) b m + 2 I b s + 2 c z + 2 p z)/(2 Sqrt[c + p])])/ E^(((-I) b m + 2 I b s)^2/(4 (c + p))) + (Sqrt[-c + p] (c + p) Erfi[(I b m - 2 I b s + 2 (-c + p) z)/ (2 Sqrt[-c + p])])/E^((I b m - 2 I b s)^2/(4 (-c + p))) + ((-c + p) Sqrt[c + p] Erfi[(I b m - 2 I b s + 2 c z + 2 p z)/ (2 Sqrt[c + p])])/E^((I b m - 2 I b s)^2/(4 (c + p))) + (Sqrt[-c + p] (c + p) Erfi[((-I) b m + 2 I b s + 2 (-c + p) z)/ (2 Sqrt[-c + p])])/E^(((-I) b m + 2 I b s)^2/(4 (-c + 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 2 ) z 2 - m - 2 π ( 1 - m mod 2 \$CellContext`m 2 ) ( p - c ) ( c + p ) ( 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]]]]] ( p - c ( c + p ) erfi ( 2 p z - 2 c z 2 p - c ) + ( p - c ) c + p erfi ( c + p z ) ) + 2 - m - 2 π ( p - c ) ( c + p ) 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]]]]] ( - ( 2 b s - b m ) 2 4 ( p - c ) p - c ( c + p ) erfi ( - b m + 2 b s + 2 ( p - c ) z 2 p - c ) + - ( b m - 2 b s ) 2 4 ( p - c ) p - c ( c + p ) erfi ( b m - 2 b s + 2 ( p - c ) z 2 p - c ) + - ( 2 b s - b m ) 2 4 ( c + p ) ( p - c ) c + p erfi ( - b m + 2 b s + 2 c z + 2 p z 2 c + p ) + - ( b m - 2 b s ) 2 4 ( c + p ) ( p - c ) c + p erfi ( b m - 2 b s + 2 c z + 2 p z 2 c + p ) ) /; m + Condition z p z 2 b z m c z 2 2 -1 m -2 1 2 1 -1 \$CellContext`m 2 p -1 c c p -1 Binomial m m 2 -1 p -1 c 1 2 c p Erfi 2 p z -1 2 c z 2 p -1 c 1 2 -1 p -1 c c p 1 2 Erfi c p 1 2 z 2 -1 m -2 1 2 p -1 c c p -1 s 0 m -1 2 -1 Binomial m s -1 2 b s -1 b m 2 4 p -1 c -1 p -1 c 1 2 c p Erfi -1 b m 2 b s 2 p -1 c z 2 p -1 c 1 2 -1 -1 b m -1 2 b s 2 4 p -1 c -1 p -1 c 1 2 c p Erfi b m -1 2 b s 2 p -1 c z 2 p -1 c 1 2 -1 -1 2 b s -1 b m 2 4 c p -1 p -1 c c p 1 2 Erfi -1 b m 2 b s 2 c z 2 p z 2 c p 1 2 -1 -1 b m -1 2 b s 2 4 c p -1 p -1 c c p 1 2 Erfi b m -1 2 b s 2 c z 2 p z 2 c p 1 2 -1 m SuperPlus [/itex]

 Rule Form

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

 2002-12-18