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 Cosh

 http://functions.wolfram.com/01.20.21.4623.01

 Input Form

 Integrate[E^(p z) Sinh[b Sqrt[z]] Cosh[c Sqrt[z]]^v, z] == 2^(-2 - v) Binomial[v, v/2] (1 - Mod[v, 2]) (-((b Sqrt[Pi] (Erfi[(-b + 2 p Sqrt[z])/(2 Sqrt[p])] + Erfi[(b + 2 p Sqrt[z])/(2 Sqrt[p])]))/(E^(b^2/(4 p)) p^(3/2))) + (4 E^(p z) Sinh[b Sqrt[z]])/p) - 2^(-2 - v) Sum[Binomial[v, s] ((-(1/p^(3/2))) ((Sqrt[Pi] (b + 2 c s - c v) (Erfi[(b + 2 c s - c v - 2 p Sqrt[z])/(2 Sqrt[p])] - Erfi[(b + 2 c s - c v + 2 p Sqrt[z])/(2 Sqrt[p])]))/ E^((b + 2 c s - c v)^2/(4 p))) - (1/p^(3/2)) ((Sqrt[Pi] (b + c (-2 s + v)) (Erfi[(b - 2 c s + c v - 2 p Sqrt[z])/ (2 Sqrt[p])] - Erfi[(b - 2 c s + c v + 2 p Sqrt[z])/ (2 Sqrt[p])]))/E^((b + c (-2 s + v))^2/(4 p))) - (4/p) E^(p z) (Sinh[(b + 2 c s - c v) Sqrt[z]] + Sinh[(b + 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 sinh ( 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 sinh ( b z ) p - b - b 2 4 p π ( erfi ( 2 p z - b 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 ) ) ( erfi ( b - 2 c s + c v - 2 p z 2 p ) - erfi ( 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 ) ( erfi ( b + 2 c s - c v - 2 p z 2 p ) - erfi ( b + 2 c s - c v + 2 p z 2 p ) ) ) - 4 p z ( sinh ( ( b + 2 c s - c v ) z ) + sinh ( ( 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 -1 b 2 4 p -1 1 2 Erfi 2 p z 1 2 -1 b 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 1 p 3 2 -1 -1 b c v -1 2 s 2 4 p -1 1 2 b c v -1 2 s Erfi b -1 2 c s c v -1 2 p z 1 2 2 p 1 2 -1 -1 Erfi b -1 2 c s c v 2 p z 1 2 2 p 1 2 -1 -1 1 p 3 2 -1 -1 b 2 c s -1 c v 2 4 p -1 1 2 b 2 c s -1 c v Erfi b 2 c s -1 c v -1 2 p z 1 2 2 p 1 2 -1 -1 Erfi b 2 c s -1 c v 2 p z 1 2 2 p 1 2 -1 -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