Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











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/07.34.21.0032.01









  


  








Input Form





Subscript[\[DoubleStruckG], 4] == ((p - q) Re[\[Alpha] + Subscript[c, g] - 1] - r Re[\[Mu]] > -((3 r)/2) /; 1 <= g <= t)








Standard Form





Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "4"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]], RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", SubscriptBox["c", "g"], "-", "1"]], "]"]]]], "-", RowBox[List["r", " ", RowBox[List["Re", "[", "\[Mu]", "]"]]]]]], ">", RowBox[List["-", FractionBox[RowBox[List["3", "r"]], "2"]]]]], "/;", RowBox[List["1", "\[LessEqual]", "g", "\[LessEqual]", "t"]]]], ")"]]]]]]








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> 4 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> p </mi> <mo> - </mo> <mi> q </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#945; </mi> <mo> + </mo> <msub> <mi> c </mi> <mi> g </mi> </msub> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> r </mi> <mo> &#8290; </mo> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#956; </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &gt; </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> r </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> <mo> /; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> g </mi> <mo> &#8804; </mo> <mi> t </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <ci> Condition </ci> <apply> <gt /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> <apply> <real /> <apply> <plus /> <ci> &#945; </ci> <apply> <ci> Subscript </ci> <ci> c </ci> <ci> g </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> r </ci> <apply> <real /> <ci> &#956; </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> r </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> g </ci> <ci> t </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "4"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["p", "-", "q"]], ")"]], " ", RowBox[List["Re", "[", RowBox[List["\[Alpha]", "+", SubscriptBox["c", "g"], "-", "1"]], "]"]]]], "-", RowBox[List["r", " ", RowBox[List["Re", "[", "\[Mu]", "]"]]]]]], ">", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["3", " ", "r"]], ")"]]]]]], "/;", RowBox[List["1", "\[LessEqual]", "g", "\[LessEqual]", "t"]]]]]]]]


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





2001-10-29