  
| 
 | 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   http://functions.wolfram.com/03.01.26.0019.01
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
 | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
    BesselJ[-\[Nu], Sqrt[z]] BesselJ[\[Nu], Sqrt[z]] == 
 (1/Sqrt[Pi]) MeijerG[{{1/2}, {}}, {{0}, {\[Nu], -\[Nu]}}, z] 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", SqrtBox["z"]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", SqrtBox["z"]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox["1", SqrtBox["\[Pi]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["\[Nu]", ",", RowBox[List["-", "\[Nu]"]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]]]]]] 
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
    
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
  
  | 
 
  | 
   
   <math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'>  <semantics>  <mrow>  <mrow>  <mrow>  <msub>  <mi> J </mi>  <mrow>  <mo> - </mo>  <mi> ν </mi>  </mrow>  </msub>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ⁢ </mo>  <mrow>  <msub>  <mi> J </mi>  <mi> ν </mi>  </msub>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <msqrt>  <mi> z </mi>  </msqrt>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <msqrt>  <mi> π </mi>  </msqrt>  </mfrac>  <mo> ⁢ </mo>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 3 </mn>  </mrow>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 1 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> z </mi>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mi> ν </mi>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mi> ν </mi>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["1", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox["\[Nu]", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", "\[Nu]"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <times />  <apply>  <times />  <apply>  <ci> Subscript </ci>  <ci> J </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> ν </ci>  </apply>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  <apply>  <times />  <apply>  <ci> Subscript </ci>  <ci> J </ci>  <ci> ν </ci>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <cn type='rational'> 1 <sep /> 2 </cn>  </list>  <list />  </list>  <list>  <list>  <cn type='integer'> 0 </cn>  </list>  <list>  <ci> ν </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> ν </ci>  </apply>  </list>  </list>  <ci> z </ci>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
 
  |   
  |  
  |  
  |   
  |  |  
  |   
  |  
  |  
  |   
  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", SqrtBox["z_"]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List["\[Nu]_", ",", SqrtBox["z_"]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["1", "2"], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List["\[Nu]", ",", RowBox[List["-", "\[Nu]"]]]], "}"]]]], "}"]], ",", "z"]], "]"]], SqrtBox["\[Pi]"]]]]]]  |  
  |  
  |   
  |  
  |  
  | 
  
  
 |  
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  | 
   Date Added to functions.wolfram.com (modification date)
   |   
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
  
  | 
 
  
  | 
  
  | 
 
  
  | 
  
  | 
  
  | 
 
 | 
  | 
  
  
  
 |  
 
 |