html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4612.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18