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/07.34.21.0092.01

 Input Form

 Integrate[\[Tau]^(\[Alpha] - 1) BesselY[\[Nu], b \[Tau]] 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]^((2 l)/k)], {\[Tau], 0, Infinity}] == ((k^\[Mu] (2 l)^(\[Alpha] - 1))/(b^\[Alpha] (2 Pi)^(SuperStar[c] (k - 1)))) MeijerG[{{(1 - (\[Alpha] + \[Nu])/2)/l, \[Ellipsis], (l - (\[Alpha] + \[Nu])/2)/l, (1 - (\[Alpha] - \[Nu])/2)/l, \[Ellipsis], (l - (\[Alpha] - \[Nu])/2)/l, Subscript[a, 1]/k, \[Ellipsis], (Subscript[a, 1] + k - 1)/k, \[Ellipsis], Subscript[a, n]/k, \[Ellipsis], (Subscript[a, n] + k - 1)/k}, {Subscript[a, n + 1]/k, \[Ellipsis], (Subscript[a, n + 1] + k - 1)/k, \[Ellipsis], Subscript[a, p]/k, \[Ellipsis], (Subscript[a, p] + k - 1)/ k, (3 - \[Alpha] + \[Nu])/(2 l), \[Ellipsis], ((1 - \[Alpha] + \[Nu])/2 + l)/l}}, {{Subscript[b, 1]/k, \[Ellipsis], (Subscript[b, 1] + k - 1)/k, \[Ellipsis], Subscript[b, m]/k, \[Ellipsis], (Subscript[b, m] + k - 1)/ k}, {Subscript[b, m + 1]/k, \[Ellipsis], (Subscript[b, m + 1] + k - 1)/ k, \[Ellipsis], Subscript[b, q]/k, \[Ellipsis], (Subscript[b, q] + k - 1)/k, (3 - \[Alpha] + \[Nu])/(2 l), \[Ellipsis], ((1 - \[Alpha] + \[Nu])/2 + l)/l}}, (\[Omega]^k (2 l)^(2 l))/ (b^(2 l) k^(k (q - p)))] /; Element[k, Integers] && k > 0 && Element[l, Integers] && l > 0 && GCD[k, l] == 1 && (\[DoubleStruckCapitalC]\[DoubleStruckCapitalC] /; \[Alpha] -> \[Alpha]/2 && \[Sigma] == b^2/4 && s == 2 && t == 0 && u == 1 && v == 3 && Subscript[c, 1] == Subscript[d, 3] == (1 - \[Nu])/2 && Subscript[d, 1] == -(\[Nu]/2) && Subscript[d, 2] == \[Nu]/2)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[SuperscriptBox["\[Tau]", RowBox[List["\[Alpha]", "-", "1"]]], RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", RowBox[List["b", " ", "\[Tau]"]]]], "]"]], 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"]]], "}"]]]], "}"]], ",", RowBox[List["\[Omega]", " ", SuperscriptBox["\[Tau]", FractionBox[RowBox[List["2", "l"]], "k"]]]]]], "]"]], RowBox[List["\[DifferentialD]", "\[Tau]"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["k", "\[Mu]"], SuperscriptBox[RowBox[List["(", RowBox[List["2", "l"]], ")"]], RowBox[List["\[Alpha]", "-", "1"]]], SuperscriptBox["b", RowBox[List["-", "\[Alpha]"]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["2", "\[Pi]"]], ")"]], RowBox[List[SuperscriptBox["c", "*"], RowBox[List["(", RowBox[List["k", "-", "1"]], ")"]]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]]]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["l", "-", RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]]]], "l"], ",", FractionBox[RowBox[List["1", "-", RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "-", "\[Nu]"]], ")"]], "/", "2"]]]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["l", "-", RowBox[List[RowBox[List["(", RowBox[List["\[Alpha]", "-", "\[Nu]"]], ")"]], "/", "2"]]]], "l"], ",", FractionBox[SubscriptBox["a", "1"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["a", "n"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "n"], "+", "k", "-", "1"]], "k"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["a", "p"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "k", "-", "1"]], "k"], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["b", "1"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["b", "m"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "m"], "+", "k", "-", "1"]], "k"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["b", "q"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "k", "-", "1"]], "k"], ",", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox["\[Omega]", "k"], SuperscriptBox[RowBox[List["(", RowBox[List["2", "l"]], ")"]], RowBox[List["2", "l"]]]]], RowBox[List[SuperscriptBox["b", RowBox[List["2", "l"]]], SuperscriptBox["k", RowBox[List["k", RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]]]]]]]]]], "]"]]]]]], "/;", 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[RowBox[List["GCD", "[", RowBox[List["k", ",", "l"]], "]"]], "\[Equal]", "1"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["\[DoubleStruckCapitalC]\[DoubleStruckCapitalC]", "/;", "\[Alpha]"]], "\[Rule]", RowBox[List[FractionBox["\[Alpha]", "2"], "\[And]", RowBox[List["\[Sigma]", "\[Equal]", FractionBox[SuperscriptBox["b", "2"], "4"]]], "\[And]", RowBox[List["s", "\[Equal]", "2"]], "\[And]", RowBox[List["t", "\[Equal]", "0"]], "\[And]", RowBox[List["u", "\[Equal]", "1"]], "\[And]", RowBox[List["v", "\[Equal]", "3"]], "\[And]", RowBox[List[SubscriptBox["c", "1"], "\[Equal]", SubscriptBox["d", "3"], "\[Equal]", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"]]], "\[And]", RowBox[List[SubscriptBox["d", "1"], "\[Equal]", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "\[And]", RowBox[List[SubscriptBox["d", "2"], "\[Equal]", FractionBox["\[Nu]", "2"]]]]]]], ")"]]]]]]]]

 MathML Form

 0 τ α - 1 Y ν ( b τ ) G p , q m , n ( ω τ 2 l 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[RowBox[List["\[Omega]", " ", SuperscriptBox["\[Tau]", FractionBox[RowBox[List["2", " ", "l"]], "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 k μ ( 2 l ) α - 1 b - α ( 2 π ) c * ( k - 1 ) G k p + 3 l , k q + l k m , k n + 2 l ( ω k ( 2 l ) 2 l b 2 l k k ( q - p ) 1 - α + ν 2 l , , l - α + ν 2 l , 1 - α - ν 2 l , , l - α - ν 2 l , a 1 k , , a 1 + k - 1 k , , a n k , , a n + k - 1 k , a n + 1 k , , a n + 1 + k - 1 k , , a p k , , a p + k - 1 k , ( 3 - α + ν ) / 2 l , , ( 1 - α + ν ) / 2 + l l b 1 k , , b 1 + k - 1 k , , b m k , , b m + k - 1 k , b m + 1 k , , b m + 1 + k - 1 k , , b q k , , b q + k - 1 k , ( 3 - α + ν ) / 2 l , , ( 1 - α + ν ) / 2 + l l ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List[RowBox[List["k", " ", "p"]], "+", RowBox[List["3", "l"]]]], ",", RowBox[List[RowBox[List["k", " ", "q"]], "+", "l"]]]], RowBox[List[RowBox[List["k", " ", "m"]], ",", RowBox[List[RowBox[List["k", " ", "n"]], "+", RowBox[List["2", "l"]]]]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List[SuperscriptBox["\[Omega]", "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "l"]], ")"]], RowBox[List["2", " ", "l"]]]]], RowBox[List[SuperscriptBox["b", RowBox[List["2", " ", "l"]]], " ", SuperscriptBox["k", RowBox[List["k", " ", RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]]]]]]]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "1"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "n"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "n"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "p"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox[SubscriptBox["b", "1"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "m"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "m"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "q"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] /; k + l + gcd ( k , l ) 1 ( ℂℂ /; α "\[Rule]" α 2 σ b 2 4 s 2 t 0 u 1 v 3 c 1 d 3 1 - ν 2 d 1 - ν 2 d 2 ν 2 ) 0 τ α - 1 Y ν ( b τ ) G p , q m , n ( ω τ 2 l 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[RowBox[List["\[Omega]", " ", SuperscriptBox["\[Tau]", FractionBox[RowBox[List["2", " ", "l"]], "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 k μ ( 2 l ) α - 1 b - α ( 2 π ) c * ( k - 1 ) G k p + 3 l , k q + l k m , k n + 2 l ( ω k ( 2 l ) 2 l b 2 l k k ( q - p ) 1 - α + ν 2 l , , l - α + ν 2 l , 1 - α - ν 2 l , , l - α - ν 2 l , a 1 k , , a 1 + k - 1 k , , a n k , , a n + k - 1 k , a n + 1 k , , a n + 1 + k - 1 k , , a p k , , a p + k - 1 k , ( 3 - α + ν ) / 2 l , , ( 1 - α + ν ) / 2 + l l b 1 k , , b 1 + k - 1 k , , b m k , , b m + k - 1 k , b m + 1 k , , b m + 1 + k - 1 k , , b q k , , b q + k - 1 k , ( 3 - α + ν ) / 2 l , , ( 1 - α + ν ) / 2 + l l ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List[RowBox[List["k", " ", "p"]], "+", RowBox[List["3", "l"]]]], ",", RowBox[List[RowBox[List["k", " ", "q"]], "+", "l"]]]], RowBox[List[RowBox[List["k", " ", "m"]], ",", RowBox[List[RowBox[List["k", " ", "n"]], "+", RowBox[List["2", "l"]]]]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List[SuperscriptBox["\[Omega]", "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "l"]], ")"]], RowBox[List["2", " ", "l"]]]]], RowBox[List[SuperscriptBox["b", RowBox[List["2", " ", "l"]]], " ", SuperscriptBox["k", RowBox[List["k", " ", RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]]]]]]]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "1"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "1"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "n"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "n"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["a", "p"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["a", "p"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox[SubscriptBox["b", "1"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "1"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "m"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "m"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[SubscriptBox["b", "q"], "k"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[SubscriptBox["b", "q"], "+", "k", "-", "1"]], "k"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "l"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]], "/", "2"]], "+", "l"]], "l"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] /; k + l + gcd ( k , l ) 1 ( ℂℂ /; α "\[Rule]" α 2 σ b 2 4 s 2 t 0 u 1 v 3 c 1 d 3 1 - ν 2 d 1 - ν 2 d 2 ν 2 ) [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[RowBox[List[SuperscriptBox["\[Tau]_", RowBox[List["\[Alpha]_", "-", "1"]]], " ", RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", RowBox[List["b_", " ", "\[Tau]_"]]]], "]"]], " ", 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_"]]], "}"]]]], "}"]], ",", RowBox[List["\[Omega]_", " ", SuperscriptBox["\[Tau]_", FractionBox[RowBox[List["2", " ", "l_"]], "k"]]]]]], "]"]]]], RowBox[List["\[DifferentialD]", "\[Tau]_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["k", "\[Mu]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "l"]], ")"]], RowBox[List["\[Alpha]", "-", "1"]]], " ", SuperscriptBox["b", RowBox[List["-", "\[Alpha]"]]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "+", "\[Nu]"]], "2"]]], "l"], ",", FractionBox[RowBox[List["1", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List["l", "-", FractionBox[RowBox[List["\[Alpha]", "-", "\[Nu]"]], "2"]]], "l"], ",", FractionBox[SubscriptBox["aa", "1"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["aa", "1"], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["aa", "n"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["aa", "n"], "+", "k", "-", "1"]], "k"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["aa", "p"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["aa", "p"], "+", "k", "-", "1"]], "k"], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], RowBox[List["2", " ", "l"]]], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]]]], "+", "l"]], "l"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["bb", "1"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["bb", "1"], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["bb", "m"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["bb", "m"], "+", "k", "-", "1"]], "k"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "+", "k", "-", "1"]], "k"], ",", "\[Ellipsis]", ",", FractionBox[SubscriptBox["bb", "q"], "k"], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[SubscriptBox["bb", "q"], "+", "k", "-", "1"]], "k"], ",", FractionBox[RowBox[List["3", "-", "\[Alpha]", "+", "\[Nu]"]], RowBox[List["2", " ", "l"]]], ",", "\[Ellipsis]", ",", FractionBox[RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "\[Alpha]", "+", "\[Nu]"]], ")"]]]], "+", "l"]], "l"]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List[SuperscriptBox["\[Omega]", "k"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "l"]], ")"]], RowBox[List["2", " ", "l"]]]]], RowBox[List[SuperscriptBox["b", RowBox[List["2", " ", "l"]]], " ", SuperscriptBox["k", RowBox[List["k", " ", RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["2", " ", "\[Pi]"]], ")"]], RowBox[List[SuperscriptBox["c", "*"], " ", RowBox[List["(", RowBox[List["k", "-", "1"]], ")"]]]]]], "/;", RowBox[List[RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", ">", "0"]], "&&", RowBox[List["l", "\[Element]", "Integers"]], "&&", RowBox[List["l", ">", "0"]], "&&", RowBox[List[RowBox[List["GCD", "[", RowBox[List["k", ",", "l"]], "]"]], "\[Equal]", "1"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["\[DoubleStruckCapitalC]\[DoubleStruckCapitalC]", "/;", "\[Alpha]"]], "\[Rule]", RowBox[List[FractionBox["\[Alpha]", "2"], "&&", RowBox[List["\[Sigma]", "\[Equal]", FractionBox[SuperscriptBox["b", "2"], "4"]]], "&&", RowBox[List["s", "\[Equal]", "2"]], "&&", RowBox[List["t", "\[Equal]", "0"]], "&&", RowBox[List["u", "\[Equal]", "1"]], "&&", RowBox[List["v", "\[Equal]", "3"]], "&&", RowBox[List[SubscriptBox["c", "1"], "\[Equal]", SubscriptBox["d", "3"], "\[Equal]", FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"]]], "&&", RowBox[List[SubscriptBox["d", "1"], "\[Equal]", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "&&", RowBox[List[SubscriptBox["d", "2"], "\[Equal]", FractionBox["\[Nu]", "2"]]]]]]], ")"]]]]]]]]]]

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

 2001-10-29