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/01.20.21.4615.01

 Input Form

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

 Standard Form

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

 Rule Form

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RowBox[List["2", " ", SqrtBox[RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]]], "/;", RowBox[List[RowBox[List["v", "\[Element]", "Integers"]], "&&", RowBox[List["v", ">", "0"]]]]]]]]]]

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

 2002-12-18