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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/07.34.21.0036.01









  


  








Input Form





Subscript[\[DoubleStruckG], 8] == (Abs[\[Phi]] + 2 Re[(q - p) (v - u) \[Alpha] + r (v - u) (\[Mu] - 1) + (q - p) (\[Rho] - 1)] > 0)








Standard Form





Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "8"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "\[Phi]", "]"]], "+", RowBox[List["2", RowBox[List["Re", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], "\[Alpha]"]], "+", RowBox[List["r", RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], RowBox[List["(", RowBox[List["\[Mu]", "-", "1"]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], RowBox[List["(", RowBox[List["\[Rho]", "-", "1"]], ")"]]]]]], "]"]]]]]], ">", "0"]], ")"]]]]]]








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> 8 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> &#981; </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#961; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mi> u </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#945; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> q </mi> <mo> - </mo> <mi> p </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#956; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> r </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> v </mi> <mo> - </mo> <mi> u </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 8 </cn> </apply> <apply> <gt /> <apply> <plus /> <apply> <abs /> <ci> &#981; </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <real /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> &#961; </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> <ci> &#945; </ci> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> p </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> &#956; </ci> <cn type='integer'> -1 </cn> </apply> <ci> r </ci> <apply> <plus /> <ci> v </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> u </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "8"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "\[Phi]", "]"]], "+", RowBox[List["2", " ", RowBox[List["Re", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List["r", " ", RowBox[List["(", RowBox[List["v", "-", "u"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Mu]", "-", "1"]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["q", "-", "p"]], ")"]], " ", RowBox[List["(", RowBox[List["\[Rho]", "-", "1"]], ")"]]]]]], "]"]]]]]], ">", "0"]]]]]]


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





2001-10-29