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/07.34.06.0051.01

 Input Form

 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]}}, z] == Sum[((-1)^k/k!) MeijerG[{{Subscript[a, 1] - k, \[Ellipsis], Subscript[a, n] - k}, {Subscript[a, n + 1] - k, \[Ellipsis], Subscript[a, p] - k, -k}}, {{0, Subscript[b, 1] - k, \[Ellipsis], Subscript[b, m] - k}, {Subscript[b, m + 1] - k, \[Ellipsis], Subscript[b, q] - k}}, x E^(2 Pi I Floor[Arg[z - x]/(2 Pi)])] (z - x)^k, {k, 0, Infinity}] /; Element[m, Integers] && m >= 0 && Element[n, Integers] && n >= 0 && Element[p, Integers] && p >= 0 && Element[q, Integers] && q >= 0 && m <= q && n <= p && x < 0

 Standard Form

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 MathML Form

 G p , q m , n ( z 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["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", "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]] k = 0 ( - 1 ) k k ! G p + 1 , q + 1 m + 1 , n ( x 2 π arg ( z - x ) 2 π a 1 - k , , a n - k , a n + 1 - k , , a p - k , - k 0 , b 1 - k , , b m - k , b m + 1 - k , , b q - k ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["p", "+", "1"]], ",", RowBox[List["q", "+", "1"]]]], RowBox[List[RowBox[List["m", "+", "1"]], ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List["x", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["\[LeftFloor]", FractionBox[RowBox[List["arg", "(", RowBox[List["z", "-", "x"]], ")"]], RowBox[List["2", " ", "\[Pi]"]]], "\[RightFloor]"]]]]]]], MeijerG, Rule[Editable, True]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "n"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List[SubscriptBox["a", "p"], "-", "k"]], ",", RowBox[List["-", "k"]]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["0", ",", RowBox[List[SubscriptBox["b", "1"], "-", "k"]]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "m"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "q"], "-", "k"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] ( z - x ) k /; m n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] p q TagBox["\[DoubleStruckCapitalN]", Function[Integers]] m q n p x < 0 G p , q m , n ( z 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["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", "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]] k = 0 ( - 1 ) k k ! G p + 1 , q + 1 m + 1 , n ( x 2 π arg ( z - x ) 2 π a 1 - k , , a n - k , a n + 1 - k , , a p - k , - k 0 , b 1 - k , , b m - k , b m + 1 - k , , b q - k ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List[RowBox[List["p", "+", "1"]], ",", RowBox[List["q", "+", "1"]]]], RowBox[List[RowBox[List["m", "+", "1"]], ",", "n"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List["x", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]", " ", RowBox[List["\[LeftFloor]", FractionBox[RowBox[List["arg", "(", RowBox[List["z", "-", "x"]], ")"]], RowBox[List["2", " ", "\[Pi]"]]], "\[RightFloor]"]]]]]]], MeijerG, Rule[Editable, True]], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "n"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", RowBox[List["n", "+", "1"]]], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List[SubscriptBox["a", "p"], "-", "k"]], ",", RowBox[List["-", "k"]]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List["0", ",", RowBox[List[SubscriptBox["b", "1"], "-", "k"]]]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "m"], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", RowBox[List["m", "+", "1"]]], "-", "k"]], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "q"], "-", "k"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] ( z - x ) k /; m n TagBox["\[DoubleStruckCapitalN]", Function[Integers]] p q TagBox["\[DoubleStruckCapitalN]", Function[Integers]] m q n p x < 0 [/itex]

 Rule Form

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

 2007-05-02