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 Cosh

 http://functions.wolfram.com/01.20.21.1293.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18