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/07.34.22.0006.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MellinTransform", "[", RowBox[List[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["c", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["c", "t"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["c", RowBox[List["t", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["c", "u"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["d", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["d", "s"]]], "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["d", RowBox[List["s", "+", "1"]]], ",", "\[Ellipsis]", ",", SubscriptBox["d", "v"]]], "}"]]]], "}"]], ",", RowBox[List["\[Sigma]", " ", "\[Tau]"]]]], "]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]], ",", RowBox[List["{", 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",", 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[SuperscriptBox["\[Omega]", "k"], SuperscriptBox["k", RowBox[List["k", RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]]]]]]], RowBox[List[SuperscriptBox["\[Sigma]", "l"], SuperscriptBox["l", RowBox[List["l", RowBox[List["(", RowBox[List["u", "-", "v"]], ")"]]]]]]]]]], "]"]]]]]], "/;", 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]", 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 MathML Form

 τ [ G u , v s , t ( σ τ c 1 , , c t , c t + 1 , , c u d 1 , , d s , d s + 1 , , d v ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["u", ",", "v"]], RowBox[List["s", ",", "t"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["\[Sigma]", " ", "\[Tau]"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["c", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["c", "t"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["c", RowBox[List["t", "+", "1"]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["c", "u"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["d", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["d", "s"], MeijerG, 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, , a n + 1 + k - 1 k , , a p k , , a p + k - 1 k b 1 k , , b 1 + k - 1 k , , b m k , , b m + k - 1 k , 1 - z - c 1 l , , l - z - c 1 l , , 1 - z - c t l , , l - z - c t l , 1 - z - c t + 1 l , , l - z - c t + 1 l , , 1 - z - c u l , , l - z - c u l , b m + 1 k , , b m + 1 + k - 1 k , , b q k , , b q + k - 1 k ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List[RowBox[List["k", " ", "p"]], "+", RowBox[List["l", " ", "v"]]]], ",", RowBox[List[RowBox[List["k", " ", "q"]], "+", RowBox[List["l", " ", "u"]]]]]], RowBox[List[RowBox[List[RowBox[List["k", " ", "m"]], "+", RowBox[List["l", " ", "t"]]]], ",", RowBox[List[RowBox[List["k", " ", "n"]], "+", RowBox[List["l", " ", "s"]]]]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox[RowBox[List[SuperscriptBox["\[Omega]", "k"], " ", SuperscriptBox["k", RowBox[List["k", " ", RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]]]]]]], RowBox[List[SuperscriptBox["\[Sigma]", "l"], " ", 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 Date Added to functions.wolfram.com (modification date)

 2001-10-29