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/01.20.21.4103.01

 Input Form

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

 Standard Form

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FractionBox[RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", RowBox[List["f", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], ")"]], "/", SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", 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 ( e + d z ) cosh v ( z c + g + f z ) z 2 - v ( 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]]]]] cosh ( e + d z ) ( 1 - v mod 2 \$CellContext`v 2 ) d + 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]]]]] ( e - g ( v - 2 s ) ( c 2 ( g ( v - 2 s ) - e ) - c 2 ( v - 2 s ) 2 4 ( f ( v - 2 s ) - d ) π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z 2 f ( v - 2 s ) - d ) ( f ( v - 2 s ) - d ) 3 / 2 - 2 c z ( v - 2 s ) + 2 ( g ( v - 2 s ) - e ) + ( f ( v - 2 s ) - d ) z f ( v - 2 s ) - d + 2 ( d - f ( v - 2 s ) ) z - c ( v - 2 s ) z d - f ( v - 2 s ) - c - c 2 ( v - 2 s ) 2 4 ( d - f ( v - 2 s ) ) π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 ( f ( v - 2 s ) - d ) z 2 d - f ( v - 2 s ) ) ( d - f ( v - 2 s ) ) 3 / 2 ) - - e - g ( v - 2 s ) ( c 2 ( e + g ( v - 2 s ) ) - c 2 ( v - 2 s ) 2 4 ( d + f ( v - 2 s ) ) π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z 2 d + f ( v - 2 s ) ) ( d + f ( v - 2 s ) ) 3 / 2 - 2 c z ( v - 2 s ) + 2 ( e + g ( v - 2 s ) ) + ( d + f ( v - 2 s ) ) z d + f ( v - 2 s ) + 2 ( - d - f ( v - 2 s ) ) z - c ( v - 2 s ) z - d - f ( v - 2 s ) - c - c 2 ( v - 2 s ) 2 4 ( - d - f ( v - 2 s ) ) π ( v - 2 s ) erfi ( c ( v - 2 s ) + 2 ( d + f ( v - 2 s ) ) z 2 - d - f ( v - 2 s ) ) ( - d - f ( v - 2 s ) ) 3 / 2 ) ) /; v + Condition z e d z z 1 2 c g f z v 2 -1 v Binomial v v 2 -1 e d z 1 -1 \$CellContext`v 2 d -1 2 -1 v -2 s 0 v -1 2 -1 Binomial v s e -1 g v -1 2 s c 2 g v -1 2 s -1 e -1 c 2 v -1 2 s 2 4 f v -1 2 s -1 d -1 1 2 v -1 2 s Erfi c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 f v -1 2 s -1 d 1 2 -1 f v -1 2 s -1 d 3 2 -1 -1 2 c z 1 2 v -1 2 s 2 g v -1 2 s -1 e f v -1 2 s -1 d z f v -1 2 s -1 d -1 2 d -1 f v -1 2 s z -1 c v -1 2 s z 1 2 d -1 f v -1 2 s -1 -1 c -1 c 2 v -1 2 s 2 4 d -1 f v -1 2 s -1 1 2 v -1 2 s Erfi c v -1 2 s 2 f v -1 2 s -1 d z 1 2 2 d -1 f v -1 2 s 1 2 -1 d -1 f v -1 2 s 3 2 -1 -1 -1 e -1 g v -1 2 s c 2 e g v -1 2 s -1 c 2 v -1 2 s 2 4 d f v -1 2 s -1 1 2 v -1 2 s Erfi c v -1 2 s 2 d f v -1 2 s z 1 2 2 d f v -1 2 s 1 2 -1 d f v -1 2 s 3 2 -1 -1 2 c z 1 2 v -1 2 s 2 e g v -1 2 s d f v -1 2 s z d f v -1 2 s -1 2 -1 d -1 f v -1 2 s z -1 c v -1 2 s z 1 2 -1 d -1 f v -1 2 s -1 -1 c -1 c 2 v -1 2 s 2 4 -1 d -1 f v -1 2 s -1 1 2 v -1 2 s Erfi c v -1 2 s 2 d f v -1 2 s z 1 2 2 -1 d -1 f v -1 2 s 1 2 -1 -1 d -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[RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["-", "v"]]], " ", RowBox[List["Cosh", "[", RowBox[List["e", "+", RowBox[List["d", " ", "z"]]]], "]"]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Mod", "[", RowBox[List["v", ",", "2"]], "]"]]]], ")"]]]], "d"], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["s", "=", "0"]], 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18