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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/07.34.21.0043.01









  


  








Input Form





Subscript[\[DoubleStruckG], 15] == (Subscript[\[Lambda], c] > 0 || (Subscript[\[Lambda], c] == 0 && Subscript[\[Lambda], s] != 0 && Re[\[Eta]] > -1) || (Subscript[\[Lambda], c] == Subscript[\[Lambda], s] == 0 && Re[\[Eta]] > 0))








Standard Form





Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckG]", "15"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[SubscriptBox["\[Lambda]", "c"], ">", "0"]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "c"], "\[Equal]", "0"]], "\[And]", RowBox[List[SubscriptBox["\[Lambda]", "s"], "\[NotEqual]", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "\[Eta]", "]"]], ">", RowBox[List["-", "1"]]]]]], ")"]], "\[Or]", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "c"], "\[Equal]", SubscriptBox["\[Lambda]", "s"], "\[Equal]", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "\[Eta]", "]"]], ">", "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> 15 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <msub> <mi> &#955; </mi> <mi> c </mi> </msub> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8744; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#955; </mi> <mi> c </mi> </msub> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> &#955; </mi> <mi> s </mi> </msub> <mo> &#8800; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#951; </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8744; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msub> <mi> &#955; </mi> <mi> c </mi> </msub> <mo> &#10869; </mo> <msub> <mi> &#955; </mi> <mi> s </mi> </msub> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#951; </mi> <mo> ) </mo> </mrow> <mo> &gt; </mo> <mn> 0 </mn> </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'> 15 </cn> </apply> <apply> <or /> <apply> <gt /> <apply> <ci> Subscript </ci> <ci> &#955; </ci> <ci> c </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#955; </ci> <ci> c </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> &#955; </ci> <ci> s </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <real /> <ci> &#951; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <and /> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#955; </ci> <ci> c </ci> </apply> <apply> <ci> Subscript </ci> <ci> &#955; </ci> <ci> s </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <real /> <ci> &#951; </ci> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "15"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "c"], ">", "0"]], "||", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "c"], "\[Equal]", "0"]], "&&", RowBox[List[SubscriptBox["\[Lambda]", "s"], "\[NotEqual]", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Eta]", "]"]], ">", RowBox[List["-", "1"]]]]]], ")"]], "||", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[Lambda]", "c"], "\[Equal]", SubscriptBox["\[Lambda]", "s"], "\[Equal]", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Eta]", "]"]], ">", "0"]]]], ")"]]]]]]]]


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





2001-10-29