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/01.20.21.4050.01

 Input Form

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

 Standard Form

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"s"]], "+", "v"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", 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

 sinh ( z b + d z ) cosh v ( c z ) z 2 - v - 2 ( 4 cosh ( z b + d z ) d + b b 2 4 d π erfi ( b + 2 d z 2 - d ) ( - d ) 3 / 2 - b - b 2 4 d π erfi ( b + 2 d z 2 d ) d 3 / 2 ) ( v v 2 ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["v", Identity, Rule[Editable, True]]], List[TagBox[FractionBox["v", "2"], Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 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, Rule[Editable, True]]], List[TagBox["s", Identity, Rule[Editable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False]] ( 4 cosh ( z b + ( d - 2 c s + c v ) z ) d + c ( v - 2 s ) + 4 cosh ( z b + ( d + 2 c s - c v ) z ) d + 2 c s - c v + b - b 2 4 ( - d - c ( v - 2 s ) ) π erfi ( b + 2 ( d + c ( v - 2 s ) ) z 2 - d - c ( v - 2 s ) ) ( - d - c ( v - 2 s ) ) 3 / 2 + b - b 2 4 ( d - c ( v - 2 s ) ) π erfi ( 2 ( c ( v - 2 s ) - d ) z - b 2 d - c ( v - 2 s ) ) ( d - c ( v - 2 s ) ) 3 / 2 - b - b 2 4 ( c ( v - 2 s ) - d ) π erfi ( 2 ( c ( v - 2 s ) - d ) z - b 2 c ( v - 2 s ) - d ) ( c ( v - 2 s ) - d ) 3 / 2 - b - b 2 4 ( d + c ( v - 2 s ) ) π erfi ( b + 2 ( d + c ( v - 2 s ) ) z 2 d + c ( v - 2 s ) ) ( d + c ( v - 2 s ) ) 3 / 2 ) /; v + Condition z z 1 2 b d z c z v 2 -1 v -2 4 z 1 2 b d z d -1 b b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 b -1 b 2 4 d -1 1 2 Erfi b 2 d z 1 2 2 d 1 2 -1 d 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 z 1 2 b d -1 2 c s c v z d c v -1 2 s -1 4 z 1 2 b d 2 c s -1 c v z d 2 c s -1 c v -1 b -1 b 2 4 -1 d -1 c v -1 2 s -1 1 2 Erfi b 2 d c v -1 2 s z 1 2 2 -1 d -1 c v -1 2 s 1 2 -1 -1 d -1 c v -1 2 s 3 2 -1 b -1 b 2 4 d -1 c v -1 2 s -1 1 2 Erfi 2 c v -1 2 s -1 d z 1 2 -1 b 2 d -1 c v -1 2 s 1 2 -1 d -1 c v -1 2 s 3 2 -1 -1 b -1 b 2 4 c v -1 2 s -1 d -1 1 2 Erfi 2 c v -1 2 s -1 d z 1 2 -1 b 2 c v -1 2 s -1 d 1 2 -1 c v -1 2 s -1 d 3 2 -1 -1 b -1 b 2 4 d c v -1 2 s -1 1 2 Erfi b 2 d c v -1 2 s z 1 2 2 d c v -1 2 s 1 2 -1 d c 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["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]], "]"]], " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "v_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], "-", "v"]]], " ", RowBox[List["Binomial", "[", RowBox[List["v", ",", FractionBox["v", "2"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]]]], "d"], "+", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["b", "2"], RowBox[List["4", " ", "d"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", 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 Date Added to functions.wolfram.com (modification date)

 2002-12-18