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/01.20.21.3735.01

 Input Form

 Integrate[E^(p Sqrt[z]) Sin[b Sqrt[z]] Cosh[c z]^v, z] == (1/(b^2 + p^2)^2) (2^(1 - v) E^(p Sqrt[z]) Binomial[v, v/2] (1 - Mod[v, 2]) (b (2 p - b^2 Sqrt[z] - p^2 Sqrt[z]) Cos[b Sqrt[z]] + (-p^2 + b^2 (1 + p Sqrt[z]) + p^3 Sqrt[z]) Sin[b Sqrt[z]])) - I 2^(-2 - v) Sum[Binomial[v, s] ((8 I E^(p Sqrt[z]) Sin[b Sqrt[z]] Sinh[c (2 s - v) z])/(c (2 s - v)) + (E^((-b + I p)^2/(c (8 s - 4 v))) (I b + p) Sqrt[Pi] Erfi[((-I) b - p + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (2 s - v)])])/ (c (2 s - v))^(3/2) - (E^((b + I p)^2/(c (8 s - 4 v))) ((-I) b + p) Sqrt[Pi] Erfi[(I b - p + 2 c (-2 s + v) Sqrt[z])/ (2 Sqrt[c (2 s - v)])])/(c (2 s - v))^(3/2) + (E^(I Pi - (b + I p)^2/(c (8 s - 4 v))) ((-I) b + p) Sqrt[Pi] Erfi[((-I) b + p + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (-2 s + v)])])/ (c (2 s - v) Sqrt[c (-2 s + v)]) - (E^((-I) Pi - (I b + p)^2/(4 c (-2 s + v))) (I b + p) Sqrt[Pi] Erfi[(I b + p + 2 c (-2 s + v) Sqrt[z])/(2 Sqrt[c (-2 s + v)])])/ (c (2 s - v) Sqrt[c (-2 s + v)])), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

 p z sin ( b z ) cosh v ( c z ) z 1 ( b 2 + p 2 ) 2 ( 2 1 - v p z ( 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 ) ( b ( - z b 2 + 2 p - p 2 z ) cos ( b z ) + ( z p 3 - p 2 + b 2 ( z p + 1 ) ) sin ( b z ) ) ) - 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]]]]] ( ( p - b ) 2 c ( 8 s - 4 v ) ( b + p ) π erfi ( - b - p + 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) ( c ( 2 s - v ) ) 3 / 2 + π - ( b + p ) 2 c ( 8 s - 4 v ) ( - b + p ) π erfi ( - b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) c ( 2 s - v ) c ( v - 2 s ) + 8 p z sin ( b z ) sinh ( c ( 2 s - v ) z ) c ( 2 s - v ) - ( b + p ) 2 c ( 8 s - 4 v ) ( - b + p ) π erfi ( b - p + 2 c ( v - 2 s ) z 2 c ( 2 s - v ) ) ( c ( 2 s - v ) ) 3 / 2 - - ( b + p ) 2 4 c ( v - 2 s ) - π ( b + p ) π erfi ( b + p + 2 c ( v - 2 s ) z 2 c ( v - 2 s ) ) c ( 2 s - v ) c ( v - 2 s ) ) /; v + Condition z p z 1 2 b z 1 2 c z v 1 b 2 p 2 2 -1 2 1 -1 v p z 1 2 Binomial v v 2 -1 1 -1 \$CellContext`v 2 b -1 z 1 2 b 2 2 p -1 p 2 z 1 2 b z 1 2 z 1 2 p 3 -1 p 2 b 2 z 1 2 p 1 b z 1 2 -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s p -1 b 2 c 8 s -1 4 v -1 b p 1 2 Erfi -1 b -1 p 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 c 2 s -1 v 3 2 -1 -1 b p 2 c 8 s -1 4 v -1 -1 b p 1 2 Erfi -1 b p 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 c 2 s -1 v c v -1 2 s 1 2 -1 8 p z 1 2 b z 1 2 c 2 s -1 v z c 2 s -1 v -1 -1 b p 2 c 8 s -1 4 v -1 -1 b p 1 2 Erfi b -1 p 2 c v -1 2 s z 1 2 2 c 2 s -1 v 1 2 -1 c 2 s -1 v 3 2 -1 -1 -1 b p 2 4 c v -1 2 s -1 -1 b p 1 2 Erfi b p 2 c v -1 2 s z 1 2 2 c v -1 2 s 1 2 -1 c 2 s -1 v 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