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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 > Major 39 groups of conditions of convergence of generalization of classical Meijer's integral from two G functions





http://functions.wolfram.com/07.34.21.0047.01









  


  








Input Form





Subscript[\[DoubleStruckCapitalC], 4] == (p == q && u == v && SuperStar[b] == SuperStar[c] == 0 && \[Sigma] > 0 && \[Omega] > 0 && Re[\[Mu]] < 1 && Re[\[Rho]] < 1 && \[Sigma]^l != \[Omega]^k && Subscript[\[DoubleStruckG], 1] && Subscript[\[DoubleStruckG], 2] && Subscript[\[DoubleStruckG], 3])








Standard Form





Cell[BoxData[RowBox[List[SubscriptBox["\[DoubleStruckCapitalC]", "4"], "\[Equal]", RowBox[List["(", RowBox[List[RowBox[List["p", "\[Equal]", "q"]], "\[And]", RowBox[List["u", "\[Equal]", "v"]], "\[And]", RowBox[List[SuperscriptBox["b", "*"], "\[Equal]", SuperscriptBox["c", "*"], "\[Equal]", "0"]], "\[And]", RowBox[List["\[Sigma]", ">", "0"]], "\[And]", RowBox[List["\[Omega]", ">", "0"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "\[Mu]", "]"]], "<", "1"]], "\[And]", RowBox[List[RowBox[List["Re", "[", "\[Rho]", "]"]], "<", "1"]], "\[And]", RowBox[List[SuperscriptBox["\[Sigma]", "l"], "\[NotEqual]", SuperscriptBox["\[Omega]", "k"]]], "\[And]", SubscriptBox["\[DoubleStruckG]", "1"], "\[And]", SubscriptBox["\[DoubleStruckG]", "2"], "\[And]", SubscriptBox["\[DoubleStruckG]", "3"]]], ")"]]]]]]








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> &#8450; </mi> <mn> 4 </mn> </msub> <mo> &#10869; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> p </mi> <mo> &#10869; </mo> <mi> q </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> u </mi> <mo> &#10869; </mo> <mi> v </mi> </mrow> <mo> &#8743; </mo> <mrow> <msup> <mi> b </mi> <mo> * </mo> </msup> <mo> &#10869; </mo> <msup> <mi> c </mi> <mo> * </mo> </msup> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#963; </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#969; </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#956; </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> &#961; </mi> <mo> ) </mo> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msup> <mi> &#963; </mi> <mi> l </mi> </msup> <mo> &#8800; </mo> <msup> <mi> &#969; </mi> <mi> k </mi> </msup> </mrow> <mo> &#8743; </mo> <msub> <mi> &#120152; </mi> <mn> 1 </mn> </msub> <mo> &#8743; </mo> <msub> <mi> &#120152; </mi> <mn> 2 </mn> </msub> <mo> &#8743; </mo> <msub> <mi> &#120152; </mi> <mn> 3 </mn> </msub> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> Subscript </ci> <ci> &#8450; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <and /> <apply> <eq /> <ci> p </ci> <ci> q </ci> </apply> <apply> <eq /> <ci> u </ci> <ci> v </ci> </apply> <apply> <eq /> <apply> <ci> SuperStar </ci> <ci> b </ci> </apply> <apply> <ci> SuperStar </ci> <ci> c </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> &#963; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <ci> &#969; </ci> <cn type='integer'> 0 </cn> </apply> <apply> <lt /> <apply> <real /> <ci> &#956; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <lt /> <apply> <real /> <ci> &#961; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <neq /> <apply> <power /> <ci> &#963; </ci> <ci> l </ci> </apply> <apply> <power /> <ci> &#969; </ci> <ci> k </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> &#120152; </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SubscriptBox["$Failed", "4"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["p", "\[Equal]", "q"]], "&&", RowBox[List["u", "\[Equal]", "v"]], "&&", RowBox[List[SuperscriptBox["b", "*"], "\[Equal]", SuperscriptBox["c", "*"], "\[Equal]", "0"]], "&&", RowBox[List["\[Sigma]", ">", "0"]], "&&", RowBox[List["\[Omega]", ">", "0"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Mu]", "]"]], "<", "1"]], "&&", RowBox[List[RowBox[List["Re", "[", "\[Rho]", "]"]], "<", "1"]], "&&", RowBox[List[SuperscriptBox["\[Sigma]", "l"], "\[NotEqual]", SuperscriptBox["\[Omega]", "k"]]], "&&", SubscriptBox["\[DoubleStruckG]", "1"], "&&", SubscriptBox["\[DoubleStruckG]", "2"], "&&", SubscriptBox["\[DoubleStruckG]", "3"]]]]]]]


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





2001-10-29