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}={1,2,3,5}





http://functions.wolfram.com/07.35.03.0161.01









  


  








Input Form





MeijerG[{{a, 1/2 + a}, {b}}, {{-(1/2) + b}, {c, b, 1/2 + 2 a - b, 2 a - c}}, z, 1/2] == (z^(2 a) BesselI[-(1/2) + b - c, z] BesselI[-(1/2) - 2 a + b + c, z])/Sqrt[Pi]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", ",", RowBox[List[FractionBox["1", "2"], "+", "a"]]]], "}"]], ",", RowBox[List["{", "b", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "b"]], "}"]], ",", RowBox[List["{", RowBox[List["c", ",", "b", ",", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["2", " ", "a"]], "-", "b"]], ",", RowBox[List[RowBox[List["2", " ", "a"]], "-", "c"]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", "a"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "b", "-", "c"]], ",", "z"]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", RowBox[List["2", " ", "a"]], "+", "b", "+", "c"]], ",", "z"]], "]"]]]], SqrtBox["\[Pi]"]]]]]]








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> 3 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mrow> <mn> 1 </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> 2 </mn> </mfrac> </mrow> <mo> &#10072; </mo> <mtable> <mtr> <mtd> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> b </mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mi> b </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mi> c </mi> <mo> , </mo> <mi> b </mi> <mo> , </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> c </mi> </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;3&quot;, &quot;,&quot;, &quot;5&quot;]], RowBox[List[&quot;1&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;2&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;1&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;b&quot;, MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[RowBox[List[&quot;b&quot;, &quot;-&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;c&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[&quot;b&quot;, MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;a&quot;]], &quot;-&quot;, &quot;b&quot;, &quot;+&quot;, FractionBox[&quot;1&quot;, &quot;2&quot;]]], MeijerG, Rule[Editable, True]], &quot;,&quot;, TagBox[RowBox[List[RowBox[List[&quot;2&quot;, &quot; &quot;, &quot;a&quot;]], &quot;-&quot;, &quot;c&quot;]], MeijerG, Rule[Editable, True]]]]]]]]], &quot;)&quot;]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> <mo> &#10869; </mo> <mrow> <mfrac> <msup> <mi> z </mi> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> </msup> <msqrt> <mi> &#960; </mi> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mrow> <mi> b </mi> <mo> - </mo> <mi> c </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> I </mi> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> c </mi> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </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'> 1 <sep /> 2 </cn> </apply> </list> <list> <ci> b </ci> </list> </list> <list> <list> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </list> <list> <ci> c </ci> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> </list> </list> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> </apply> <apply> <power /> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> BesselI </ci> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <ci> BesselI </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <ci> b </ci> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </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["1", "2"], "+", "a_"]]]], "}"]], ",", RowBox[List["{", "b_", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "b_"]], "}"]], ",", RowBox[List["{", RowBox[List["c_", ",", "b_", ",", RowBox[List[FractionBox["1", "2"], "+", RowBox[List["2", " ", "a_"]], "-", "b_"]], ",", RowBox[List[RowBox[List["2", " ", "a_"]], "-", "c_"]]]], "}"]]]], "}"]], ",", "z_", ",", FractionBox["1", "2"]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["2", " ", "a"]]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "b", "-", "c"]], ",", "z"]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", RowBox[List["2", " ", "a"]], "+", "b", "+", "c"]], ",", "z"]], "]"]]]], SqrtBox["\[Pi]"]]]]]]


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





2003-08-21