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/07.34.06.0010.01

 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] \[Proportional] 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]}}, (-1)^(m + n - q)] (1 + O[z - (-1)^(m + n - q)]) + Pi^(m + n - q - 1) Gamma[-Subscript[\[Psi], q]] Sum[(Product[Sin[(Subscript[a, k] - Subscript[b, h]) Pi], {k, n + 1, q}]/ Product[If[k == h, 1, Sin[(Subscript[b, k] - Subscript[b, h]) Pi]], {k, 1, m}]) E^((m + n - q) Pi I Subscript[b, h]) (1 - (-1)^(q - m - n) z)^Subscript[\[Psi], q] (1 + O[z - (-1)^(m + n - q)]), {h, 1, m}] /; (z -> (-1)^(m + n - q)) && 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]

 Standard Form

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 MathML Form

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( z "\[Rule]" ( - 1 ) m + n - q ) "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 ( ψ q - μ j = 1 q ( a j - b j ) - 1 /; p q ) ψ q TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] 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]] G q , q m , n ( ( - 1 ) m + n - q 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[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "+", "n", "-", "q"]]], 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]] ( 1 + O ( z - ( - 1 ) m + n - q ) ) + π m + n - q - 1 Γ ( - ψ q ) h = 1 m ( m + n - q ) π b h k = n + 1 q sin ( ( a k - b h ) π ) k = 1 k h m sin ( ( b k - b h ) π ) ( 1 - ( - 1 ) q - m - n z ) ψ q ( 1 + O ( z - ( - 1 ) m + n - q ) ) /; ( z "\[Rule]" ( - 1 ) m + n - q ) "\[LeftBracketingBar]" z "\[RightBracketingBar]" < 1 ( ψ q - μ j = 1 q ( a j - b j ) - 1 /; p q ) ψ q TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] [/itex]

 Rule Form

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

 2001-10-29