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| Hypergeometric Functions  MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z,r]  Specific values  Specialized values  Case {m,n,p,q}={0,2,2,2}   |  |  
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 | | http://functions.wolfram.com/07.35.03.0021.01 | 
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 | | MeijerG[{{a, c}, {}}, {{}, {b, -a + b + c}}, z, 1/2] == 
 ((Gamma[1 + b - c] UnitStep[-1 + Abs[z]])/Gamma[2 a - b - c]) 
  z^(-2 + 2 a - b + c) (1 - z^(-2))^(-1 + 2 a - 2 b) 
  GegenbauerC[b - c, a - b, (1 + z^2)/(2 z)] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", ",", "c"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["b", ",", RowBox[List[RowBox[List["-", "a"]], "+", "b", "+", "c"]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "+", "b", "-", "c"]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z", "]"]]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "-", "c"]], "]"]]], SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["2", " ", "a"]], "-", "b", "+", "c"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", SuperscriptBox["z", RowBox[List["-", "2"]]]]], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["GegenbauerC", "[", RowBox[List[RowBox[List["b", "-", "c"]], ",", RowBox[List["a", "-", "b"]], ",", FractionBox[RowBox[List["1", "+", SuperscriptBox["z", "2"]]], RowBox[List["2", " ", "z"]]]]], "]"]]]]]]]] | 
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   <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> 2 </mn>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mn> 2 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> z </mi>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mrow>  <mi> a </mi>  <mo> , </mo>  <mi> c </mi>  </mrow>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mi> b </mi>  <mo> , </mo>  <mrow>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  <mo> - </mo>  <mi> a </mi>  </mrow>  </mrow>  </mtd>  </mtr>  </mtable>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["0", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["a", MeijerG, Rule[Editable, True]], ",", TagBox["c", MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "+", "c", "-", "a"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  <mo> ⩵ </mo>  <mrow>  <mfrac>  <mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <semantics>  <mi> θ </mi>  <annotation-xml encoding='MathML-Content'>  <ci> UnitStep </ci>  </annotation-xml>  </semantics>  <mo> ( </mo>  <mrow>  <mrow>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[LeftBracketingBar]" </annotation>  </semantics>  <mi> z </mi>  <semantics>  <mo> ❘ </mo>  <annotation encoding='Mathematica'> "\[RightBracketingBar]" </annotation>  </semantics>  </mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> - </mo>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> - </mo>  <mi> b </mi>  <mo> + </mo>  <mi> c </mi>  <mo> - </mo>  <mn> 2 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <msup>  <mrow>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mfrac>  </mrow>  <mo> ) </mo>  </mrow>  <mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> - </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> b </mi>  </mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <msubsup>  <mi> C </mi>  <mrow>  <mi> b </mi>  <mo> - </mo>  <mi> c </mi>  </mrow>  <mrow>  <mi> a </mi>  <mo> - </mo>  <mi> b </mi>  </mrow>  </msubsup>  <mo> ( </mo>  <mfrac>  <mrow>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mo> + </mo>  <mn> 1 </mn>  </mrow>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </mfrac>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <ci> MeijerG </ci>  <list>  <list>  <ci> a </ci>  <ci> c </ci>  </list>  <list />  </list>  <list>  <list />  <list>  <ci> b </ci>  <apply>  <plus />  <ci> b </ci>  <ci> c </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  </list>  </list>  <ci> z </ci>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <times />  <apply>  <times />  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  <cn type='integer'> 1 </cn>  </apply>  </apply>  <apply>  <ci> UnitStep </ci>  <apply>  <plus />  <apply>  <abs />  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <ci> Gamma </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>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <power />  <ci> z </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>  <ci> c </ci>  <cn type='integer'> -2 </cn>  </apply>  </apply>  <apply>  <power />  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> a </ci>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> b </ci>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <apply>  <power />  <apply>  <ci> Subscript </ci>  <ci> C </ci>  <apply>  <plus />  <ci> b </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> c </ci>  </apply>  </apply>  </apply>  <apply>  <plus />  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> b </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 1 </cn>  </apply>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Date Added to functions.wolfram.com (modification date) | 
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 | | MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] |  |  | 
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