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/01.20.21.4054.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b", " ", SqrtBox["z"]]], "]"]], SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], "v"], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox["b", "2"]], RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "v"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "b"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", SqrtBox["z"]]]]], ")"]]]], "+", RowBox[List["b", " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", 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"-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "f"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], ")"]], RowBox[List["3", "/", "2"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", RowBox[List["2", " ", "f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["f", " ", 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

 sinh ( b z ) cosh v ( g + f z ) z 2 - v - b z ( z b + 2 b z ( b z - 1 ) + 1 ) ( 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 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]]]]] ( - g ( v - 2 s ) ( 4 g ( v - 2 s ) cosh ( z b + ( 2 s - v ) ( g + f z ) ) f ( 2 s - v ) + b b 2 4 f ( v - 2 s ) π erfi ( 2 f ( v - 2 s ) z - b 2 - f ( v - 2 s ) ) ( - f ( v - 2 s ) ) 3 / 2 - b 2 g ( v - 2 s ) - b 2 4 f ( v - 2 s ) π erfi ( 2 f ( v - 2 s ) z - b 2 f ( v - 2 s ) ) ( f ( v - 2 s ) ) 3 / 2 ) - - g ( v - 2 s ) ( 4 g ( v - 2 s ) cosh ( b z - ( 2 s - v ) ( g + f z ) ) f ( 2 s - v ) + b 2 g ( v - 2 s ) - b 2 4 f ( v - 2 s ) π erfi ( b + 2 f ( v - 2 s ) z 2 f ( v - 2 s ) ) ( f ( v - 2 s ) ) 3 / 2 - b b 2 4 f ( v - 2 s ) π erfi ( b + 2 f ( v - 2 s ) z 2 - f ( v - 2 s ) ) ( - f ( v - 2 s ) ) 3 / 2 ) ) /; v + Condition z b z 1 2 g f z v 2 -1 v -1 b z 1 2 z 1 2 b 2 b z 1 2 b z 1 2 -1 1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 b 2 -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s -1 g v -1 2 s 4 g v -1 2 s z 1 2 b 2 s -1 v g f z f 2 s -1 v -1 b b 2 4 f v -1 2 s -1 1 2 Erfi 2 f v -1 2 s z 1 2 -1 b 2 -1 f v -1 2 s 1 2 -1 -1 f v -1 2 s 3 2 -1 -1 b 2 g v -1 2 s -1 b 2 4 f v -1 2 s -1 1 2 Erfi 2 f v -1 2 s z 1 2 -1 b 2 f v -1 2 s 1 2 -1 f v -1 2 s 3 2 -1 -1 -1 g v -1 2 s 4 g v -1 2 s b z 1 2 -1 2 s -1 v g f z f 2 s -1 v -1 b 2 g v -1 2 s -1 b 2 4 f v -1 2 s -1 1 2 Erfi b 2 f v -1 2 s z 1 2 2 f v -1 2 s 1 2 -1 f v -1 2 s 3 2 -1 -1 b b 2 4 f v -1 2 s -1 1 2 Erfi b 2 f v -1 2 s z 1 2 2 -1 f v -1 2 s 1 2 -1 -1 f v -1 2 s 3 2 -1 v SuperPlus [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b_", " ", SqrtBox["z_"]]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "v"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "b"]], " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", SqrtBox["z"]]]]], ")"]]]], "+", RowBox[List["b", " ", SqrtBox["z"]]]]], ")"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18