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variants of this functions
MeijerG




Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Integration > Definite integration > Generalization of classical Meijer's integral from two G functions > Fifteen subgroups for major 39 groups





http://functions.wolfram.com/07.34.21.0029.01









  


  








Input Form





Subscript[\[DoubleStruckG], 1] == (( !(Element[Subscript[a, i] - Subscript[b, j], Integers] && Subscript[a, i] - Subscript[b, j] > 0) /; 1 <= i <= n && 1 <= j <= m) && ( !(Element[Subscript[c, g] - Subscript[d, h], Integers] && Subscript[c, g] - Subscript[d, h] > 0) /; 1 <= g <= t && 1 <= h <= s))








Standard Form





Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "1"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["b", "j"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["b", "j"]]], ">", "0"]]]], "]"]], "/;", RowBox[List[RowBox[List["1", "\[LessEqual]", "i", "\[LessEqual]", "n"]], "\[And]", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "m"]]]]]], ")"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Not", "[", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["c", "g"], "-", SubscriptBox["d", "h"]]], "\[Element]", "Integers"]], "\[And]", RowBox[List[RowBox[List[SubscriptBox["c", "g"], "-", SubscriptBox["d", "h"]]], ">", "0"]]]], "]"]], "/;", RowBox[List[RowBox[List["1", "\[LessEqual]", "g", "\[LessEqual]", "t"]], "\[And]", RowBox[List["1", "\[LessEqual]", "h", "\[LessEqual]", "s"]]]]]], ")"]]]], ")"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msub> <mi> &#120152; </mi> <mn> 1 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> a </mi> <mi> i </mi> </msub> <mo> - </mo> <msub> <mi> b </mi> <mi> j </mi> </msub> </mrow> <mo> &#8713; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> i </mi> <mo> &#8804; </mo> <mi> n </mi> </mrow> <mo> &#8743; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> j </mi> <mo> &#8804; </mo> <mi> m </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <msub> <mi> c </mi> <mi> g </mi> </msub> <mo> - </mo> <msub> <mi> d </mi> <mi> h </mi> </msub> </mrow> <mo> &#8713; </mo> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> g </mi> <mo> &#8804; </mo> <mi> t </mi> </mrow> <mo> &#8743; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> h </mi> <mo> &#8804; </mo> <mi> s </mi> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <and /> <apply> <ci> Condition </ci> <apply> <notin /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> a </ci> <ci> i </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <ci> j </ci> </apply> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <and /> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> i </ci> <ci> n </ci> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> j </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <ci> Condition </ci> <apply> <notin /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> g </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> d </ci> <ci> h </ci> </apply> </apply> </apply> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> <apply> <and /> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> g </ci> <ci> t </ci> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> h </ci> <ci> s </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "1"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["b", "j"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[SubscriptBox["a", "i"], "-", SubscriptBox["b", "j"]]], ">", "0"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["1", "\[LessEqual]", "i", "\[LessEqual]", "n"]], "&&", RowBox[List["1", "\[LessEqual]", "j", "\[LessEqual]", "m"]]]]]], ")"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["c", "g"], "-", SubscriptBox["d", "h"]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List[SubscriptBox["c", "g"], "-", SubscriptBox["d", "h"]]], ">", "0"]]]], ")"]]]], "/;", RowBox[List[RowBox[List["1", "\[LessEqual]", "g", "\[LessEqual]", "t"]], "&&", RowBox[List["1", "\[LessEqual]", "h", "\[LessEqual]", "s"]]]]]], ")"]]]]]]]]


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





2001-10-29