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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] > Integral transforms > Mellin transforms





http://functions.wolfram.com/07.34.22.0005.01









  


  








Input Form





MellinTransform[MeijerG[{{}, {}}, {{}, {}}, t x], t, z] == x^(-z) /; x > 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MellinTransform", "[", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["t", " ", "x"]]]], "]"]], ",", "t", ",", "z"]], "]"]], "\[Equal]", SuperscriptBox["x", RowBox[List["-", "z"]]]]], "/;", RowBox[List["x", ">", "0"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <msub> <mi> &#8499; </mi> <mi> t </mi> </msub> <mo> [ </mo> <mrow> <msubsup> <semantics> <mi> G </mi> <annotation encoding='Mathematica'> TagBox[&quot;G&quot;, MeijerG] </annotation> </semantics> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <semantics> <mrow> <mi> t </mi> <mo> &#8290; </mo> <mi> x </mi> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[&quot;t&quot;, &quot; &quot;, &quot;x&quot;]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <semantics> <mo> &#8202; </mo> <annotation encoding='Mathematica'> TagBox[&quot;\[Null]&quot;, MeijerG, Rule[Editable, False]] </annotation> </semantics> </mtd> </mtr> <mtr> <mtd> <semantics> <mo> &#8202; </mo> <annotation encoding='Mathematica'> TagBox[&quot;\[Null]&quot;, MeijerG, Rule[Editable, False]] </annotation> </semantics> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ] </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> &#10869; </mo> <msup> <mi> x </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubscriptBox </ci> <ms> &#8499; </ms> <ms> t </ms> </apply> <ms> [ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> G </ms> <ci> MeijerG </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> 0 </ms> <ms> , </ms> <ms> 0 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 0 </ms> <ms> , </ms> <ms> 0 </ms> </list> </apply> </apply> <ms> &#8289; </ms> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <apply> <ci> RowBox </ci> <list> <ms> t </ms> <ms> </ms> <ms> x </ms> </list> </apply> <ci> MeijerG </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <true /> </apply> </apply> <ms> &#10072; </ms> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> TagBox </ci> <ms> &#62368; </ms> <ci> MeijerG </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> </apply> </list> <list> <apply> <ci> TagBox </ci> <ms> &#62368; </ms> <ci> MeijerG </ci> <apply> <ci> Rule </ci> <ci> Editable </ci> <false /> </apply> </apply> </list> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ] </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <ms> z </ms> <ms> ) </ms> </list> </apply> </list> </apply> <ms> &#10869; </ms> <apply> <ci> SuperscriptBox </ci> <ms> x </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> z </ms> </list> </apply> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> x </ms> <ms> &gt; </ms> <ms> 0 </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MellinTransform", "[", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["t_", " ", "x_"]]]], "]"]], ",", "t_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["x", RowBox[List["-", "z"]]], "/;", RowBox[List["x", ">", "0"]]]]]]]]


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





2001-10-29