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,r] > Specific values > Specialized values > Case {m,n,p,q}={2,2,4,2}





http://functions.wolfram.com/07.35.03.0139.01









  


  








Input Form





MeijerG[{{a, 2/3 + a}, {1/2 + a, 7/6 + a}}, {{1/12 + a, 7/12 + a}, {}}, z, 1/3] == -4 (2/3)^(1/6) Pi z^(1/2 + 3 a) AiryAiPrime[(3/2)^(2/3)/z] Sinh[1/z^(3/2)]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", ",", RowBox[List[FractionBox["2", "3"], "+", "a"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "a"]], ",", RowBox[List[FractionBox["7", "6"], "+", "a"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "12"], "+", "a"]], ",", RowBox[List[FractionBox["7", "12"], "+", "a"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "3"]]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["1", "/", "6"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["3", " ", "a"]]]]], " ", RowBox[List["AiryAiPrime", "[", FractionBox[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], "z"], "]"]], " ", RowBox[List["Sinh", "[", FractionBox["1", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "]"]]]]]]]]








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> <mn> 4 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> z </mi> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 7 </mn> <mn> 6 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 12 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 7 </mn> <mn> 12 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox[&quot;G&quot;, MeijerG], RowBox[List[&quot;4&quot;, &quot;,&quot;, &quot;2&quot;]], RowBox[List[&quot;2&quot;, &quot;,&quot;, &quot;2&quot;]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[RowBox[List[TagBox[&quot;z&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[&quot;1&quot;, &quot;3&quot;], MeijerG, Rule[Editable, True]]]], MeijerG], &quot;\[VerticalSeparator]&quot;, GridBox[List[List[RowBox[List[TagBox[&quot;a&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;2&quot;, &quot;3&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;7&quot;, &quot;6&quot;]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;12&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[&quot;a&quot;, &quot;+&quot;, FractionBox[&quot;7&quot;, &quot;12&quot;]]], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> <mo> &#8290; </mo> <mroot> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mn> 6 </mn> </mroot> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mn> 1 </mn> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> Ai </mi> <mo> &#8242; </mo> </msup> <mo> ( </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> / </mo> <mn> 3 </mn> </mrow> </msup> <mi> z </mi> </mfrac> <mo> ) </mo> </mrow> <mtext> </mtext> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> MeijerG </ci> <list> <list> <ci> a </ci> <apply> <plus /> <ci> a </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </list> <list> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='rational'> 7 <sep /> 6 </cn> </apply> </list> </list> <list> <list> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 12 </cn> </apply> <apply> <plus /> <ci> a </ci> <cn type='rational'> 7 <sep /> 12 </cn> </apply> </list> <list /> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 3 </cn> </apply> <apply> <times /> <cn type='integer'> -4 </cn> <pi /> <apply> <power /> <cn type='rational'> 2 <sep /> 3 </cn> <cn type='rational'> 1 <sep /> 6 </cn> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <sinh /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> AiryAiPrime </ci> <apply> <times /> <apply> <power /> <cn type='rational'> 3 <sep /> 2 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </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["a_", ",", RowBox[List[FractionBox["2", "3"], "+", "a_"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "a_"]], ",", RowBox[List[FractionBox["7", "6"], "+", "a_"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "12"], "+", "a_"]], ",", RowBox[List[FractionBox["7", "12"], "+", "a_"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z_", ",", FractionBox["1", "3"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "4"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "3"], ")"]], RowBox[List["1", "/", "6"]]], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["3", " ", "a"]]]]], " ", RowBox[List["AiryAiPrime", "[", FractionBox[SuperscriptBox[RowBox[List["(", FractionBox["3", "2"], ")"]], RowBox[List["2", "/", "3"]]], "z"], "]"]], " ", RowBox[List["Sinh", "[", FractionBox["1", SuperscriptBox["z", RowBox[List["3", "/", "2"]]]], "]"]]]]]]]]


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





2001-10-29