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 Cosh

 http://functions.wolfram.com/01.20.21.3736.01

 Input Form

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

 Standard Form

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 MathML Form

 p z 2 sin ( b z ) cosh v ( c z ) z 2 - v - 2 π ( 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 2 - 2 π p 4 p erfi ( - b + 2 p z 2 p ) + - 2 π p - b 2 4 p erfi ( b + 2 p z 2 p ) ) ( 1 - v mod 2 \$CellContext`v 2 ) p + 1 p ( 2 - v - 2 π 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]]]]] ( - ( - b + c ( v - 2 s ) ) 2 - 2 π p 4 p erfi ( - b + c ( v - 2 s ) + 2 p z 2 p ) + - ( b + c ( v - 2 s ) ) 2 + 2 π p 4 p erfi ( b + c ( v - 2 s ) + 2 p z 2 p ) + - ( - b - c ( v - 2 s ) ) 2 - 2 π p 4 p erfi ( - b - c ( v - 2 s ) + 2 p z 2 p ) + - ( b - c ( v - 2 s ) ) 2 + 2 π p 4 p erfi ( b - c ( v - 2 s ) + 2 p z 2 p ) ) ) /; v TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] v > 0 Condition z p z 2 b z c z v 2 -1 v -2 1 2 Binomial v v 2 -1 -1 -1 b 2 -1 2 p 4 p -1 Erfi -1 b 2 p z 2 p 1 2 -1 -1 2 p -1 b 2 4 p -1 Erfi b 2 p z 2 p 1 2 -1 1 -1 \$CellContext`v 2 p 1 2 -1 1 p 1 2 -1 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s -1 -1 b c v -1 2 s 2 -1 2 p 4 p -1 Erfi -1 b c v -1 2 s 2 p z 2 p 1 2 -1 -1 b c v -1 2 s 2 2 p 4 p -1 Erfi b c v -1 2 s 2 p z 2 p 1 2 -1 -1 -1 b -1 c v -1 2 s 2 -1 2 p 4 p -1 Erfi -1 b -1 c v -1 2 s 2 p z 2 p 1 2 -1 -1 b -1 c v -1 2 s 2 2 p 4 p -1 Erfi b -1 c v -1 2 s 2 p z 2 p 1 2 -1 v v 0 [/itex]

 Rule Form

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

 2002-12-18