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] > Specific values > Specialized values > Cases with arbitrary {m,n,p,q} > Case {m,n,p,q}={1,n,n,n+1}





http://functions.wolfram.com/07.34.03.0035.01









  


  








Input Form





MeijerG[{{Subscript[a, 1], \[Ellipsis], Subscript[a, n]}, {}}, {{0}, {Subscript[a, 1] + 1, \[Ellipsis], Subscript[a, n] + 1}}, z] == -D[Nest[z D[#1, z] & , E^(-z), n], z] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n] == -1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "n"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a", "1"], "+", "1"]], ",", "\[Ellipsis]", ",", RowBox[List[SubscriptBox["a", "n"], "+", "1"]]]], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["-", RowBox[List[SubscriptBox["\[PartialD]", "z"], " ", RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["z", " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], "#1"]]]], "&"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], ",", "n"]], "]"]]]]]]]], "/;", RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", "n"], "\[Equal]", RowBox[List["-", "1"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> n </mi> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;n&quot;, &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;n&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mtext> </mtext> <mstyle scriptlevel='0'> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mtext> </mtext> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mfrac> <mi> d </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mstyle> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mi> n </mi> <mo> , </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mrow> <mn> 1 </mn> <mo> , </mo> <mi> n </mi> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 0 </mn> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mo> &#8230; </mo> <mo> , </mo> <mn> 0 </mn> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;n&quot;, &quot;,&quot;, RowBox[List[&quot;n&quot;, &quot;+&quot;, &quot;1&quot;]]]], RowBox[List[&quot;1&quot;, &quot;,&quot;, &quot;n&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;-&quot;, &quot;1&quot;]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;\[Ellipsis]&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;0&quot;, MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, True]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mtext> </mtext> <mstyle scriptlevel='0'> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <mi> d </mi> <mtext> </mtext> </mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <munderover> <mo> &#8719; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mfrac> <mi> d </mi> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mstyle> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", "\[Ellipsis]_", ",", SubscriptBox["a_", "n_"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[SubscriptBox["a_", "1"], "+", "1"]], ",", "\[Ellipsis]_", ",", RowBox[List[SubscriptBox["a_", "n_"], "+", "1"]]]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], RowBox[List["Nest", "[", RowBox[List[RowBox[List[RowBox[List["z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z"]]], "#1"]]]], "&"]], ",", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], ",", "n"]], "]"]]]]]], "/;", RowBox[List[SubscriptBox["a", "1"], "\[Equal]", SubscriptBox["a", "2"], "\[Equal]", "\[Ellipsis]", "\[Equal]", SubscriptBox["a", "n"], "\[Equal]", RowBox[List["-", "1"]]]]]]]]]]


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





2001-10-29