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 Cosh

 http://functions.wolfram.com/01.20.21.4618.01

 Input Form

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

 Standard Form

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"Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z sinh ( b z ) cosh v ( c z 2 ) z 2 - v p z ( 1 - v mod 2 \$CellContext`v 2 ) ( b cosh ( b z ) - p sinh ( b z ) ) ( p - b ) ( b + p ) ( 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]]]]] - 2 - v - 2 π c s = 0 v - 1 2 1 v - 2 s ( ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["s", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( ( p - b ) 2 + 2 c π ( v - 2 s ) 4 c ( v - 2 s ) - c ( v - 2 s ) erfi ( - b + p - 2 c ( v - 2 s ) z 2 - c ( v - 2 s ) ) + ( b + p ) 2 - 2 c π ( v - 2 s ) 4 c ( v - 2 s ) - c ( v - 2 s ) erfi ( b + p - 2 c ( v - 2 s ) z 2 - c ( v - 2 s ) ) - - ( p - b ) 2 - 2 c π ( v - 2 s ) 4 c ( v - 2 s ) c ( v - 2 s ) erfi ( - b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) - - ( b + p ) 2 + 2 c π ( v - 2 s ) 4 c ( v - 2 s ) c ( v - 2 s ) erfi ( b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) ) ) /; v + Condition z p z b z c z 2 v 2 -1 v p z 1 -1 \$CellContext`v 2 b b z -1 p b z p -1 b b p -1 Binomial v v 2 -1 -1 2 -1 v -2 1 2 c -1 s 0 v -1 2 -1 1 v -1 2 s -1 Binomial v s p -1 b 2 2 c v -1 2 s 4 c v -1 2 s -1 -1 c v -1 2 s 1 2 Erfi -1 b p -1 2 c v -1 2 s z 2 -1 c v -1 2 s 1 2 -1 b p 2 -1 2 c v -1 2 s 4 c v -1 2 s -1 -1 c v -1 2 s 1 2 Erfi b p -1 2 c v -1 2 s z 2 -1 c v -1 2 s 1 2 -1 -1 -1 p -1 b 2 -1 2 c v -1 2 s 4 c v -1 2 s -1 c v -1 2 s 1 2 Erfi -1 b p 2 c v -1 2 s z 2 c v -1 2 s 1 2 -1 -1 -1 b p 2 2 c v -1 2 s 4 c v -1 2 s -1 c v -1 2 s 1 2 Erfi b p 2 c v -1 2 s z 2 c v -1 2 s 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18