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 Cosh

 http://functions.wolfram.com/01.20.21.4628.01

 Input Form

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

 Standard Form

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 MathML Form

 b z 2 + e sinh ( a z 2 + q ) cosh v ( c z 2 + g ) z 2 - v - 2 e - q π ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 2 q erfi ( a + b z ) a + b - erfi ( b - a z ) b - a ) ( 1 - v mod 2 \$CellContext`v 2 ) - 2 - v - 2 π s = 0 v - 1 2 ( v s ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( e - q + g ( v - 2 s ) - π 2 erfi ( - a + b + c ( v - 2 s ) z ) - a + b + c ( v - 2 s ) + e + q + g ( v - 2 s ) + π 2 erfi ( a + b + c ( v - 2 s ) z ) a + b + c ( v - 2 s ) + e - q - g ( v - 2 s ) - π 2 erfi ( - a + b - c ( v - 2 s ) z ) - a + b - c ( v - 2 s ) + e + q - g ( v - 2 s ) + π 2 erfi ( a + b - c ( v - 2 s ) z ) a + b - c ( v - 2 s ) ) /; v + Condition z b z 2 e a z 2 q c z 2 g v 2 -1 v -2 e -1 q 1 2 Binomial v v 2 -1 2 q Erfi a b 1 2 z a b 1 2 -1 -1 Erfi b -1 a 1 2 z b -1 a 1 2 -1 1 -1 \$CellContext`v 2 -1 2 -1 v -2 1 2 s 0 v -1 2 -1 Binomial v s e -1 q g v -1 2 s -1 2 -1 Erfi -1 a b c v -1 2 s 1 2 z -1 a b c v -1 2 s 1 2 -1 e q g v -1 2 s 2 -1 Erfi a b c v -1 2 s 1 2 z a b c v -1 2 s 1 2 -1 e -1 q -1 g v -1 2 s -1 2 -1 Erfi -1 a b -1 c v -1 2 s 1 2 z -1 a b -1 c v -1 2 s 1 2 -1 e q -1 g v -1 2 s 2 -1 Erfi a b -1 c v -1 2 s 1 2 z a b -1 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