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/07.34.06.0009.01

 Input Form

 MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {Subscript[a, n + 1], \[Ellipsis], Subscript[a, q]}}, {{Subscript[b, 1], \[Ellipsis], Subscript[b, m]}, {Subscript[b, m + 1], \[Ellipsis], Subscript[b, q]}}, z] == (-(Pi^(m + n - q)/Sin[Subscript[\[Psi], q] Pi])) Sum[z^(Subscript[a, h] - 1) ((-1)^(q - m - n) z)^(1 - Subscript[a, h]) (Product[Sin[(Subscript[a, h] - Subscript[b, k]) Pi], {k, m + 1, q}]/ Product[If[k == h, 1, Sin[(Subscript[a, h] - Subscript[a, k]) Pi]], {k, 1, n}]) (MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, q]}, {}}, {{}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}}, (-1)^(q - m - n) z] - (1/Pi^2) Sum[Sin[(Subscript[a, h] - Subscript[a, j]) Pi] (Product[Sin[(Subscript[b, k] - Subscript[a, j]) Pi], {k, 1, q}]/ Product[If[k == j, 1, Sin[(Subscript[a, k] - Subscript[a, j]) Pi]], {k, 1, q}]) MeijerG[{{Subscript[a, h], Subscript[a, j]}, {Subscript[a, 1], \[Ellipsis], Subscript[a, q]}}, {{Subscript[a, h], Subscript[a, j], Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, {}}, (-1)^(q - m - n) z], {j, 1, q}]), {h, 1, n}] /; Abs[z] > 1 && (Subscript[\[Psi], q] == -\[Mu] == Sum[Subscript[a, j] - Subscript[b, j], {j, 1, q}] - 1 /; p == q) && !Element[Subscript[\[Psi], q], Integers] && m n != 0

 Standard Form

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 MathML Form

 G q , q m , n ( z a 1 , , a n , a n + 1 , , a q b 1 , , b m , b m + 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["q", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", 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", "q"], 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]] - π m + n - q sin ( ψ q π ) h = 1 n ( z a h - 1 ( ( - 1 ) q - m - n z ) 1 - a h k = m + 1 q sin ( ( a h - b k ) π ) k = 1 k h n sin ( ( a h - a k ) π ) ( G q , q 0 , q ( ( - 1 ) q - m - n z a 1 , , a q b 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["q", ",", "q"]], RowBox[List["0", ",", "q"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["q", "-", "m", "-", "n"]]], " ", "z"]], 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", "q"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] - 1 π 2 j = 1 q sin ( ( a h - a j ) π ) k = 1 q sin ( ( b k - a j ) π ) k = 1 k j q sin ( ( a k - a j ) π ) G q + 2 , q + 2 q + 2 , 2 ( ( - 1 ) q - m - n z a h , a j , a 1 , , a q a h , a j , b 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["q", "+", "2"]], ",", RowBox[List["q", "+", "2"]]]], RowBox[List[RowBox[List["q", "+", "2"]], ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["q", "-", "m", "-", "n"]]], " ", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "h"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "j"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "q"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["a", "h"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "j"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] ) ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 ( ψ q - μ j = 1 q ( a j - b j ) - 1 /; p q ) ψ q TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m n 0 G q , q m , n ( z a 1 , , a n , a n + 1 , , a q b 1 , , b m , b m + 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["q", ",", "q"]], RowBox[List["m", ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", 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", "q"], 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]] - π m + n - q sin ( ψ q π ) h = 1 n ( z a h - 1 ( ( - 1 ) q - m - n z ) 1 - a h k = m + 1 q sin ( ( a h - b k ) π ) k = 1 k h n sin ( ( a h - a k ) π ) ( G q , q 0 , q ( ( - 1 ) q - m - n z a 1 , , a q b 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["q", ",", "q"]], RowBox[List["0", ",", "q"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["q", "-", "m", "-", "n"]]], " ", "z"]], 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", "q"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] - 1 π 2 j = 1 q sin ( ( a h - a j ) π ) k = 1 q sin ( ( b k - a j ) π ) k = 1 k j q sin ( ( a k - a j ) π ) G q + 2 , q + 2 q + 2 , 2 ( ( - 1 ) q - m - n z a h , a j , a 1 , , a q a h , a j , b 1 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["q", "+", "2"]], ",", RowBox[List["q", "+", "2"]]]], RowBox[List[RowBox[List["q", "+", "2"]], ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["q", "-", "m", "-", "n"]]], " ", "z"]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "h"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "j"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "q"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["a", "h"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "j"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] ) ) /; "\[LeftBracketingBar]" z "\[RightBracketingBar]" > 1 ( ψ q - μ j = 1 q ( a j - b j ) - 1 /; p q ) ψ q TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] m n 0 [/itex]

 Rule Form

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

 2001-10-29