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/01.20.21.4619.01

 Input Form

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

 Standard Form

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SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c", " ", "s"]], "-", RowBox[List["c", " ", "v"]]]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "+", "p"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "p"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "\[And]", RowBox[List["v", ">", "0"]]]]]]]]

 MathML Form

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