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; }

 MeijerG

 http://functions.wolfram.com/07.34.21.0096.01

 Input Form

 Integrate[(\[Tau]^(\[Alpha] - 1)/(\[Tau] + z)^\[Beta]) MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, (\[Omega] (\[Tau] + z)^l)/\[Tau]^k], {\[Tau], 0, Infinity}] == ((Sqrt[2 Pi] k^(\[Alpha] - 1/2) l^(1/2 - \[Beta]) z^(\[Alpha] - \[Beta]))/ (k - l)^(\[Alpha] - \[Beta] + 1/2)) MeijerG[{{(\[Alpha] - \[Beta] + 1)/(k - l), \[Ellipsis], (\[Alpha] - \[Beta] + k - l)/(k - l), Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, p], \[Beta]/l, \[Ellipsis], (\[Beta] + l - 1)/l}}, {{\[Alpha]/k, \[Ellipsis], (\[Alpha] + k - 1)/k, Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, ((\[Omega] l^l)/k^k) (z/(k - l))^(l - k)] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && k > l && SuperStar[c] > 0 && Abs[Arg[\[Omega] z^(l - k)]] < Pi SuperStar[c] && (k - l) Min[Re[Subscript[b, 1]], \[Ellipsis], Re[Subscript[b, m]]] + Re[\[Beta] - \[Alpha]] > 0 && k - k Max[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, n]]] + Re[\[Alpha]] > 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[SuperscriptBox["\[Tau]", RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox[RowBox[List["(", RowBox[List["\[Tau]", "+", "z"]], ")"]], "\[Beta]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["\[Omega]", SuperscriptBox[RowBox[List["(", RowBox[List["\[Tau]", "+", "z"]], ")"]], "l"]]], SuperscriptBox["\[Tau]", "k"]]]], "]"]], RowBox[List["\[DifferentialD]", "\[Tau]"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SqrtBox[RowBox[List["2", "\[Pi]"]]], SuperscriptBox["k", RowBox[List["\[Alpha]", "-", FractionBox["1", "2"]]]], SuperscriptBox["l", RowBox[List[FractionBox["1", "2"], "-", "\[Beta]"]]], SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "\[Beta]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["k", "-", "l"]], ")"]], RowBox[List["\[Alpha]", "-", "\[Beta]", "+", FractionBox["1", "2"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "1"]], RowBox[List["k", "-", "l"]]], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "k", "-", "l"]], RowBox[List["k", "-", "l"]]], ",", SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"], ",", FractionBox["\[Beta]", "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Beta]", "+", "l", "-", "1"]], "l"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Alpha]", "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "+", "k", "-", "1"]], "k"], ",", SubscriptBox["b", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List["\[Omega]", " ", SuperscriptBox["l", "l"]]], SuperscriptBox["k", "k"]], SuperscriptBox[RowBox[List["(", FractionBox["z", RowBox[List["k", "-", "l"]]], ")"]], RowBox[List["l", "-", "k"]]]]]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", ">", "0"]], "\[And]", RowBox[List["l", "\[Element]", "Integers"]], "\[And]", RowBox[List["l", ">", "0"]], "\[And]", RowBox[List["k", ">", "l"]], "\[And]", RowBox[List[SuperscriptBox["c", "*"], ">", "0"]], "\[And]", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["\[Omega]", " ", SuperscriptBox["z", RowBox[List["l", "-", "k"]]]]], "]"]], "]"]], "<", RowBox[List["\[Pi]", " ", SuperscriptBox["c", "*"]]]]], "\[And]", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["k", "-", "l"]], ")"]], RowBox[List["Min", "[", RowBox[List[RowBox[List["Re", "[", SubscriptBox["b", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Re", "[", SubscriptBox["b", "m"], "]"]]]], "]"]]]], "+", RowBox[List["Re", "[", RowBox[List["\[Beta]", "-", "\[Alpha]"]], "]"]]]], ">", "0"]], "\[And]", RowBox[List[RowBox[List["k", "-", RowBox[List["k", " ", RowBox[List["Max", "[", RowBox[List[RowBox[List["Re", "[", SubscriptBox["a", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Re", "[", SubscriptBox["a", "n"], "]"]]]], "]"]]]], "+", RowBox[List["Re", "[", "\[Alpha]", "]"]]]], ">", "0"]]]]]]]]

 MathML Form

 0 τ α - 1 ( z + τ ) β G p , q m , n ( ω ( z + τ ) l τ k a 1 , , a n , a n + 1 , , a p b 1 , , b m , b m + 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["p", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List["\[Omega]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "\[Tau]"]], ")"]], "l"]]], SuperscriptBox["\[Tau]", "k"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "n"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "m"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] τ 2 π k α - 1 2 l 1 2 - β z α - β ( k - l ) α - β + 1 2 G TagBox["G", MeijerG] p + k , q + k m + k , n + k - l ( ω l l k k ( z k - l ) l - k TagBox[RowBox[List[FractionBox[RowBox[List["\[Omega]", " ", SuperscriptBox["l", "l"]]], SuperscriptBox["k", "k"]], SuperscriptBox[RowBox[List["(", FractionBox["z", RowBox[List["k", "-", "l"]]], ")"]], RowBox[List["l", "-", "k"]]]]], MeijerG, Rule[Editable, True]] α - β + 1 k - l TagBox[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "1"]], RowBox[List["k", "-", "l"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , α - β + k - l k - l TagBox[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "k", "-", "l"]], RowBox[List["k", "-", "l"]]], MeijerG, Rule[Editable, True]] , a 1 TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , a n TagBox[SubscriptBox["a", "n"], MeijerG, Rule[Editable, True]] , a n + 1 TagBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , a p TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]] , β l TagBox[FractionBox["\[Beta]", "l"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , β + l - 1 l TagBox[FractionBox[RowBox[List["\[Beta]", "+", "l", "-", "1"]], "l"], MeijerG, Rule[Editable, True]] α k TagBox[FractionBox["\[Alpha]", "k"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , α + k - 1 k TagBox[FractionBox[RowBox[List["\[Alpha]", "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]] , b 1 TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , b m TagBox[SubscriptBox["b", "m"], MeijerG, Rule[Editable, True]] , b m + 1 TagBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , b q TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]] ) /; k + l + k > l c * > 0 "\[LeftBracketingBar]" arg ( ω z l - k ) "\[RightBracketingBar]" < π c * ( k - l ) min ( Re ( b 1 ) , , Re ( b m ) ) + Re ( β - α ) > 0 k - k max ( Re ( a 1 ) , , Re ( a n ) ) + Re ( α ) > 0 0 τ α - 1 ( z + τ ) β G p , q m , n ( ω ( z + τ ) l τ k a 1 , , a n , a n + 1 , , a p b 1 , , b m , b m + 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["p", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List["\[Omega]", " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "\[Tau]"]], ")"]], "l"]]], SuperscriptBox["\[Tau]", "k"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "n"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "m"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] τ 2 π k α - 1 2 l 1 2 - β z α - β ( k - l ) α - β + 1 2 G TagBox["G", MeijerG] p + k , q + k m + k , n + k - l ( ω l l k k ( z k - l ) l - k TagBox[RowBox[List[FractionBox[RowBox[List["\[Omega]", " ", SuperscriptBox["l", "l"]]], SuperscriptBox["k", "k"]], SuperscriptBox[RowBox[List["(", FractionBox["z", RowBox[List["k", "-", "l"]]], ")"]], RowBox[List["l", "-", "k"]]]]], MeijerG, Rule[Editable, True]] α - β + 1 k - l TagBox[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "1"]], RowBox[List["k", "-", "l"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , α - β + k - l k - l TagBox[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "k", "-", "l"]], RowBox[List["k", "-", "l"]]], MeijerG, Rule[Editable, True]] , a 1 TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , a n TagBox[SubscriptBox["a", "n"], MeijerG, Rule[Editable, True]] , a n + 1 TagBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , a p TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]] , β l TagBox[FractionBox["\[Beta]", "l"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , β + l - 1 l TagBox[FractionBox[RowBox[List["\[Beta]", "+", "l", "-", "1"]], "l"], MeijerG, Rule[Editable, True]] α k TagBox[FractionBox["\[Alpha]", "k"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , α + k - 1 k TagBox[FractionBox[RowBox[List["\[Alpha]", "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]] , b 1 TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , b m TagBox[SubscriptBox["b", "m"], MeijerG, Rule[Editable, True]] , b m + 1 TagBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], MeijerG, Rule[Editable, True]] , TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]] , b q TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]] ) /; k + l + k > l c * > 0 "\[LeftBracketingBar]" arg ( ω z l - k ) "\[RightBracketingBar]" < π c * ( k - l ) min ( Re ( b 1 ) , , Re ( b m ) ) + Re ( β - α ) > 0 k - k max ( Re ( a 1 ) , , Re ( a n ) ) + Re ( α ) > 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[Tau]_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "n_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a_", RowBox[List["n_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "p_"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "m_"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", RowBox[List["m_", "+", "1"]]], ",", "\[Ellipsis]_", ",", SubscriptBox["b_", "q_"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["\[Omega]_", " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[Tau]_", "+", "z_"]], ")"]], "l_"]]], SuperscriptBox["\[Tau]_", "k"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["\[Tau]_", "+", "z_"]], ")"]], "\[Beta]_"]], RowBox[List["\[DifferentialD]", "\[Tau]_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SuperscriptBox["k", RowBox[List["\[Alpha]", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox["l", RowBox[List[FractionBox["1", "2"], "-", "\[Beta]"]]], " ", SuperscriptBox["z", RowBox[List["\[Alpha]", "-", "\[Beta]"]]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "1"]], RowBox[List["k", "-", "l"]]], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "-", "\[Beta]", "+", "k", "-", "l"]], RowBox[List["k", "-", "l"]]], ",", SubscriptBox["aa", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "n"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["aa", "p"], ",", FractionBox["\[Beta]", "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Beta]", "+", "l", "-", "1"]], "l"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Alpha]", "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["\[Alpha]", "+", "k", "-", "1"]], "k"], ",", SubscriptBox["bb", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "m"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["bb", "q"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Omega]", " ", SuperscriptBox["l", "l"]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", RowBox[List["k", "-", "l"]]], ")"]], RowBox[List["l", "-", "k"]]]]], SuperscriptBox["k", "k"]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["k", "-", "l"]], ")"]], RowBox[List["\[Alpha]", "-", "\[Beta]", "+", FractionBox["1", "2"]]]]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]], "&&", RowBox[List["l", "\[Element]", "Integers"]], "&&", RowBox[List["l", ">", "0"]], "&&", RowBox[List["k", ">", "l"]], "&&", RowBox[List[SuperscriptBox["c", "*"], ">", "0"]], "&&", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["\[Omega]", " ", SuperscriptBox["z", RowBox[List["l", "-", "k"]]]]], "]"]], "]"]], "<", RowBox[List["\[Pi]", " ", SuperscriptBox["c", "*"]]]]], "&&", RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["k", "-", "l"]], ")"]], " ", RowBox[List["Min", "[", RowBox[List[RowBox[List["Re", "[", SubscriptBox["bb", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Re", "[", SubscriptBox["bb", "m"], "]"]]]], "]"]]]], "+", RowBox[List["Re", "[", RowBox[List["\[Beta]", "-", "\[Alpha]"]], "]"]]]], ">", "0"]], "&&", RowBox[List[RowBox[List["k", "-", RowBox[List["k", " ", RowBox[List["Max", "[", RowBox[List[RowBox[List["Re", "[", SubscriptBox["aa", "1"], "]"]], ",", "\[Ellipsis]", ",", RowBox[List["Re", "[", SubscriptBox["aa", "n"], "]"]]]], "]"]]]], "+", RowBox[List["Re", "[", "\[Alpha]", "]"]]]], ">", "0"]]]]]]]]]]

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

 2001-10-29