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 Cosh

 http://functions.wolfram.com/01.20.21.3745.01

 Input Form

 Integrate[E^(p z) Sin[b Sqrt[z]] Cosh[c Sqrt[z]]^v, z] == 2^(-2 - v) Binomial[v, v/2] (1 - Mod[v, 2]) (-((b E^(b^2/(4 p)) Sqrt[Pi] (Erfi[((-I) b + 2 p Sqrt[z])/(2 Sqrt[p])] + Erfi[(I b + 2 p Sqrt[z])/(2 Sqrt[p])]))/p^(3/2)) + (4 E^(p z) Sin[b Sqrt[z]])/p) - I 2^(-2 - v) Sum[Binomial[v, s] ((1/p^(3/2)) (E^((b + 2 I c s - I c v)^2/(4 p)) Sqrt[Pi] (b + 2 I c s - I c v) (Erf[(b + 2 I c s - I c v - 2 I p Sqrt[z])/(2 Sqrt[p])] - Erf[(b + 2 I c s - I c v + 2 I p Sqrt[z])/(2 Sqrt[p])])) + (1/p^(3/2)) (E^((b + I c (-2 s + v))^2/(4 p)) Sqrt[Pi] (b + I c (-2 s + v)) (Erf[(b - 2 I c s + I c v - 2 I p Sqrt[z])/ (2 Sqrt[p])] - Erf[(b - 2 I c s + I c v + 2 I p Sqrt[z])/ (2 Sqrt[p])])) + (1/p) (4 I E^(p z) (Sin[(b + 2 I c s - I c v) Sqrt[z]] + Sin[(b + I c (-2 s + v)) Sqrt[z]]))), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

 p z sin ( b z ) cosh v ( c z ) z 2 - v - 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]]]]] ( 1 - v mod 2 \$CellContext`v 2 ) ( 4 p z sin ( b z ) p - b b 2 4 p π ( erfi ( - b + 2 p z 2 p ) + erfi ( b + 2 p z 2 p ) ) p 3 / 2 ) - 2 - 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]]]]] ( 1 p 3 / 2 ( ( b + c ( v - 2 s ) ) 2 4 p π ( b + c ( v - 2 s ) ) ( erf ( b - 2 c s + c v - 2 p z 2 p ) - erf ( b - 2 c s + c v + 2 p z 2 p ) ) ) + 1 p 3 / 2 ( ( b + 2 c s - c v ) 2 4 p π ( b + 2 c s - c v ) ( erf ( b + 2 c s - c v - 2 p z 2 p ) - erf ( b + 2 c s - c v + 2 p z 2 p ) ) ) + 4 p z ( sin ( ( b + 2 c s - c v ) z ) + sin ( ( b + c ( v - 2 s ) ) z ) ) p ) /; v + Condition z p z b z 1 2 c z 1 2 v 2 -1 v -2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 4 p z b z 1 2 p -1 -1 b b 2 4 p -1 1 2 Erfi -1 b 2 p z 1 2 2 p 1 2 -1 Erfi b 2 p z 1 2 2 p 1 2 -1 p 3 2 -1 -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s 1 p 3 2 -1 b c v -1 2 s 2 4 p -1 1 2 b c v -1 2 s Erf b -1 2 c s c v -1 2 p z 1 2 2 p 1 2 -1 -1 Erf b -1 2 c s c v 2 p z 1 2 2 p 1 2 -1 1 p 3 2 -1 b 2 c s -1 c v 2 4 p -1 1 2 b 2 c s -1 c v Erf b 2 c s -1 c v -1 2 p z 1 2 2 p 1 2 -1 -1 Erf b 2 c s -1 c v 2 p z 1 2 2 p 1 2 -1 4 p z b 2 c s -1 c v z 1 2 b c v -1 2 s z 1 2 p -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18