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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/07.34.21.0042.01









  


  








Input Form





Subscript[\[DoubleStruckG], 14] == ((Abs[Arg[1 - Subscript[z, 0] (\[Omega]^k/\[Sigma]^l)]] < Pi /; Subscript[z, 0] == r^(l (v - u)) Exp[(-(l SuperStar[b] + k SuperStar[c])) Pi I]) && \[Phi] == 0 && SuperStar[c] + r (SuperStar[b] - 1) <= 0)








Standard Form





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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> 14 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> &#8290; </mo> <msup> <mi> &#969; </mi> <mi> k </mi> </msup> </mrow> <msup> <mi> &#963; </mi> <mi> l </mi> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mi> &#960; </mi> </mrow> <mo> /; </mo> <mrow> <msub> <mi> z </mi> <mn> 0 </mn> </msub> <mo> &#10869; </mo> <mrow> <msup> <mi> r </mi> <mrow> <mi> l </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mi> u </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> l </mi> <mo> &#8290; </mo> <msup> <mi> b </mi> <mo> * </mo> </msup> </mrow> <mo> + </mo> <mrow> <mi> k </mi> <mo> &#8290; </mo> <msup> <mi> c </mi> <mo> * </mo> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mi> &#8520; </mi> </mrow> </msup> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#981; </mi> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> b </mi> <mo> * </mo> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mo> + </mo> <msup> <mi> c </mi> <mo> * </mo> </msup> </mrow> <mo> &#8804; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 14 </cn> </apply> <apply> <and /> <apply> <ci> Condition </ci> <apply> <lt /> <apply> <abs /> <apply> <arg /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <power /> <ci> &#969; </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <power /> <ci> &#963; </ci> <ci> l </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <pi /> </apply> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <times /> <apply> <power /> <ci> r </ci> <apply> <times /> <ci> l </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <apply> <times /> <ci> l </ci> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> </apply> <apply> <times /> <ci> k </ci> <apply> <ci> SuperStar </ci> <ci> c </ci> </apply> </apply> </apply> </apply> <pi /> <imaginaryi /> </apply> </apply> </apply> </apply> </apply> <apply> <eq /> <ci> &#981; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <leq /> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> <ci> r </ci> </apply> <apply> <ci> SuperStar </ci> <ci> c </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "14"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", RowBox[List["1", "-", FractionBox[RowBox[List[SubscriptBox["z", "0"], " ", SuperscriptBox["\[Omega]", "k"]]], SuperscriptBox["\[Sigma]", "l"]]]], "]"]], "]"]], "<", "\[Pi]"]], "/;", RowBox[List[SubscriptBox["z", "0"], "\[Equal]", RowBox[List[SuperscriptBox["r", RowBox[List["l", " ", RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[RowBox[List["l", " ", SuperscriptBox["b", "*"]]], "+", RowBox[List["k", " ", SuperscriptBox["c", "*"]]]]], ")"]]]], " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]]], ")"]], "&&", RowBox[List["\[Phi]", "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List[SuperscriptBox["c", "*"], "+", RowBox[List["r", " ", RowBox[List["(", RowBox[List[SuperscriptBox["b", "*"], "-", "1"]], ")"]]]]]], "\[LessEqual]", "0"]]]]]]]]


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





2001-10-29