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/07.34.22.0004.01

 Input Form

 MellinTransform[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] t], t, z] == Product[Gamma[Subscript[b, k] + z] Product[Gamma[1 - Subscript[a, k] - z], {k, 1, n}], {k, 1, m}]/ Product[Gamma[Subscript[a, k] + z] Product[Gamma[1 - Subscript[b, k] - z], {k, m + 1, q}], {k, n + 1, p}]/ \[Omega]^z /; m^2 + n^2 > 0 && \[Omega] != 0 && ((SuperStar[c] > 0 && Abs[Arg[\[Omega]]] < SuperStar[c] Pi && -Min[Re[Subscript[b, 1]], \[Ellipsis], Re[Subscript[b, m]]] < Re[z] < 1 - Max[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, n]]]) || (p != q && SuperStar[c] >= 0 && Abs[Arg[\[Omega]]] == SuperStar[c] Pi && -Min[Re[Subscript[b, 1]], \[Ellipsis], Re[Subscript[b, m]]] < Re[z] < 1 - Max[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, n]]] && Re[\[Mu] + (q - p) z] < 3/2 && \[Mu] == Sum[Subscript[b, j], {j, 1, q}] - Sum[Subscript[a, j], {j, 1, p}] + (p - q)/2 + 1) || (p == q && SuperStar[c] == 0 && \[Omega] > 0 && -Min[Re[Subscript[b, 1]], \[Ellipsis], Re[Subscript[b, m]]] < Re[z] < 1 - Max[Re[Subscript[a, 1]], \[Ellipsis], Re[Subscript[a, n]]] && Re[Sum[Subscript[b, j] - Subscript[a, j], {j, 1, q}]] < 0))

 Standard Form

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 MathML Form

 t [ G p , q m , n ( ω t 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]", " ", "t"]], 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]] ] ( z ) ω - z k = 1 m Γ ( b k + z ) k = 1 n Γ ( 1 - a k - z ) k = n + 1 p Γ ( a k + z ) k = m + 1 q Γ ( 1 - b k - z ) /; m 2 + n 2 > 0 ω 0 ( ( c * > 0 "\[LeftBracketingBar]" arg ( ω ) "\[RightBracketingBar]" < c * π - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) ) ( p q c * 0 "\[LeftBracketingBar]" arg ( ω ) "\[RightBracketingBar]" c * π - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) Re ( ( q - p ) z + μ ) < 3 2 μ j = 1 q b j - j = 1 p a j + p - q 2 + 1 ) ( p q c * 0 ω > 0 - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) Re ( j = 1 q ( b j - a j ) ) < 0 ) ) t [ G p , q m , n ( ω t 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]", " ", "t"]], 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]] ] ( z ) ω - z k = 1 m Γ ( b k + z ) k = 1 n Γ ( 1 - a k - z ) k = n + 1 p Γ ( a k + z ) k = m + 1 q Γ ( 1 - b k - z ) /; m 2 + n 2 > 0 ω 0 ( ( c * > 0 "\[LeftBracketingBar]" arg ( ω ) "\[RightBracketingBar]" < c * π - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) ) ( p q c * 0 "\[LeftBracketingBar]" arg ( ω ) "\[RightBracketingBar]" c * π - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) Re ( ( q - p ) z + μ ) < 3 2 μ j = 1 q b j - j = 1 p a j + p - q 2 + 1 ) ( p q c * 0 ω > 0 - min ( Re ( b 1 ) , , Re ( b m ) ) < Re ( z ) < 1 - max ( Re ( a 1 ) , , Re ( a n ) ) Re ( j = 1 q ( b j - a j ) ) < 0 ) ) [/itex]

 Rule Form

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

 2001-10-29