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 Cosh

 http://functions.wolfram.com/01.20.21.1217.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18