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/01.20.21.3805.01

 Input Form

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

 Standard Form

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 MathML Form

 p z cos ( b z ) cosh v ( c z ) z 2 - v - 2 ( - - p 2 4 b p π erfi ( p - 2 b z 2 - b ) ( - b ) 3 / 2 + 4 p z sin ( b z ) b - p 2 4 b p π erfi ( p + 2 b z 2 b ) ( b ) 3 / 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 ) + 2 - v - 2 k = 0 v - 1 2 ( v k ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity]], List[TagBox["k", Identity]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]]] ( 2 p z ( 2 sinh ( ( b + 2 c k - c v ) z ) b + 2 c k - c v + 2 sinh ( ( b + c ( v - 2 k ) ) z ) b + c ( v - 2 k ) ) - - p 2 4 ( - b - 2 c k + c v ) p π erfi ( p + 2 ( - b - 2 c k + c v ) z 2 - b - 2 c k + c v ) ( - b - 2 c k + c v ) 3 / 2 - - p 2 4 ( b - 2 c k + c v ) p π erfi ( p + 2 ( b - 2 c k + c v ) z 2 b - 2 c k + c v ) ( b - 2 c k + c v ) 3 / 2 - - p 2 4 ( - b + 2 c k - c v ) p π erfi ( p + 2 ( - b + 2 c k - c v ) z 2 - b + 2 c k - c v ) ( - b + 2 c k - c v ) 3 / 2 - - p 2 4 ( b + 2 c k - c v ) p π erfi ( p + 2 ( b + 2 c k - c v ) z 2 b + 2 c k - c v ) ( b + 2 c k - c v ) 3 / 2 ) /; v + Condition z p z 1 2 b z c z v 2 -1 v -2 -1 -1 p 2 4 b -1 p 1 2 Erfi p -1 2 b z 1 2 2 -1 b 1 2 -1 -1 b 3 2 -1 4 p z 1 2 b z b -1 -1 p 2 4 b -1 p 1 2 Erfi p 2 b z 1 2 2 b 1 2 -1 b 3 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 2 -1 v -2 k 0 v -1 2 -1 Binomial v k 2 p z 1 2 2 b 2 c k -1 c v z b 2 c k -1 c v -1 2 b c v -1 2 k z b c v -1 2 k -1 -1 -1 p 2 4 -1 b -1 2 c k c v -1 p 1 2 Erfi p 2 -1 b -1 2 c k c v z 1 2 2 -1 b -1 2 c k c v 1 2 -1 -1 b -1 2 c k c v 3 2 -1 -1 -1 p 2 4 b -1 2 c k c v -1 p 1 2 Erfi p 2 b -1 2 c k c v z 1 2 2 b -1 2 c k c v 1 2 -1 b -1 2 c k c v 3 2 -1 -1 -1 p 2 4 -1 b 2 c k -1 c v -1 p 1 2 Erfi p 2 -1 b 2 c k -1 c v z 1 2 2 -1 b 2 c k -1 c v 1 2 -1 -1 b 2 c k -1 c v 3 2 -1 -1 -1 p 2 4 b 2 c k -1 c v -1 p 1 2 Erfi p 2 b 2 c k -1 c v z 1 2 2 b 2 c k -1 c v 1 2 -1 b 2 c k -1 c v 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18