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/01.20.21.3809.01

 Input Form

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

 Standard Form

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RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "b"]], "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]]]]], "/;", 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 ) v 2 - v - 1 ( - b + p ) z ( - b + p + 2 b z ( b + p ) ) ( 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 + p ) ( b + p ) + 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]]]]] ( 4 ( - b + p ) z cosh ( c ( v - 2 s ) z ) - b + p + 4 ( b + p ) z cosh ( c ( v - 2 s ) z ) b + p - c - c 2 ( v - 2 s ) 2 4 ( - b + p ) π ( v - 2 s ) erfi ( 2 z ( b - p ) + c ( v - 2 s ) 2 - b + p ) ( - b + p ) 3 / 2 - c - c 2 ( v - 2 s ) 2 4 ( - b + p ) π ( v - 2 s ) erfi ( 2 z ( - b + p ) + c ( v - 2 s ) 2 - b + p ) ( - b + p ) 3 / 2 - c - c 2 ( v - 2 s ) 2 4 ( b + p ) π ( v - 2 s ) erfi ( 2 z ( - b - p ) + c ( v - 2 s ) 2 b + p ) ( b + p ) 3 / 2 - c - c 2 ( v - 2 s ) 2 4 ( b + p ) π ( v - 2 s ) erfi ( 2 z ( b + p ) + c ( v - 2 s ) 2 b + p ) ( b + p ) 3 / 2 ) /; v + Condition z p z b z c z 1 2 v -1 v 2 -1 v -1 -1 b p z -1 b p 2 b z b p Binomial v v 2 -1 1 -1 \$CellContext`v 2 b p b p -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s 4 -1 b p z c v -1 2 s z 1 2 -1 b p -1 4 b p z c v -1 2 s z 1 2 b p -1 -1 c -1 c 2 v -1 2 s 2 4 -1 b p -1 1 2 v -1 2 s Erfi 2 z 1 2 b -1 p c v -1 2 s 2 -1 b p 1 2 -1 -1 b p 3 2 -1 -1 c -1 c 2 v -1 2 s 2 4 -1 b p -1 1 2 v -1 2 s Erfi 2 z 1 2 -1 b p c v -1 2 s 2 -1 b p 1 2 -1 -1 b p 3 2 -1 -1 c -1 c 2 v -1 2 s 2 4 b p -1 1 2 v -1 2 s Erfi 2 z 1 2 -1 b -1 p c v -1 2 s 2 b p 1 2 -1 b p 3 2 -1 -1 c -1 c 2 v -1 2 s 2 4 b p -1 1 2 v -1 2 s Erfi 2 z 1 2 b p c v -1 2 s 2 b p 1 2 -1 b p 3 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18