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/01.20.21.3803.01

 Input Form

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

 Standard Form

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" ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]], "]"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "k"]], "-", "v"]], ")"]], " ", SqrtBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "k"]], "+", "v"]], ")"]]]]]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18