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   http://functions.wolfram.com/01.03.26.0198.01
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    E^((Pi I a)/2 - z) Gamma[a, -z] + E^(-((Pi I a)/2) + z) Gamma[a, z] == 
  (1/(Sqrt[Pi] Gamma[1 - a])) MeijerG[{{a/2}, {}}, {{0, 1/2, a/2}, {}}, 
    Sqrt[-z^2]/2, 1/2] /; Inequality[0, Less, Arg[z], LessEqual, Pi] 
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   Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "a"]], "2"], "-", "z"]]], " ", RowBox[List["Gamma", "[", RowBox[List["a", ",", RowBox[List["-", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "a"]], "2"]]], "+", "z"]]], " ", RowBox[List["Gamma", "[", RowBox[List["a", ",", "z"]], "]"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["1", " "]], RowBox[List[SqrtBox["\[Pi]"], RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["a", "2"], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["a", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "2"], ",", FractionBox["1", "2"]]], "]"]]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]] 
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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>  <mrow>  <mrow>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mfrac>  <mrow>  <mi> π </mi>  <mo> ⁢ </mo>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mn> 2 </mn>  </mfrac>  <mo> - </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> , </mo>  <mrow>  <mo> - </mo>  <mi> z </mi>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mi> π </mi>  <mo> ⁢ </mo>  <mi> ⅈ </mi>  <mo> ⁢ </mo>  <mi> a </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> , </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo>  </mo>  <mrow>  <mfrac>  <mn> 1 </mn>  <mrow>  <msqrt>  <mi> π </mi>  </msqrt>  <mo> ⁢ </mo>  <mrow>  <mi> Γ </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mn> 1 </mn>  <mo> - </mo>  <mi> a </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <semantics>  <mrow>  <msubsup>  <mi> G </mi>  <mrow>  <mn> 1 </mn>  <mo> , </mo>  <mn> 3 </mn>  </mrow>  <mrow>  <mn> 3 </mn>  <mo> , </mo>  <mn> 1 </mn>  </mrow>  </msubsup>  <mo> ⁡ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mfrac>  <msqrt>  <mrow>  <mo> - </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  </mrow>  </msqrt>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  </mrow>  <mo> ❘ </mo>  <mtable>  <mtr>  <mtd>  <mfrac>  <mi> a </mi>  <mn> 2 </mn>  </mfrac>  </mtd>  </mtr>  <mtr>  <mtd>  <mrow>  <mn> 0 </mn>  <mo> , </mo>  <mfrac>  <mn> 1 </mn>  <mn> 2 </mn>  </mfrac>  <mo> , </mo>  <mfrac>  <mi> a </mi>  <mn> 2 </mn>  </mfrac>  </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["3", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[TagBox[FractionBox["a", "2"], MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["a", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation>  </semantics>  </mrow>  </mrow>  <mo> /; </mo>  <mrow>  <mn> 0 </mn>  <mo> < </mo>  <mrow>  <mi> arg </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mi> z </mi>  <mo> ) </mo>  </mrow>  <mo> ≤ </mo>  <mi> π </mi>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <plus />  <apply>  <times />  <pi />  <imaginaryi />  <ci> a </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <ci> a </ci>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <plus />  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <times />  <pi />  <imaginaryi />  <ci> a </ci>  </apply>  </apply>  <ci> z </ci>  </apply>  </apply>  <apply>  <ci> Gamma </ci>  <ci> a </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <apply>  <power />  <pi />  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <ci> Gamma </ci>  <apply>  <plus />  <cn type='integer'> 1 </cn>  <apply>  <times />  <cn type='integer'> -1 </cn>  <ci> a </ci>  </apply>  </apply>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <ci> MeijerG </ci>  <list>  <list>  <apply>  <times />  <ci> a </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </list>  <list />  </list>  <list>  <list>  <cn type='integer'> 0 </cn>  <cn type='rational'> 1 <sep /> 2 </cn>  <apply>  <times />  <ci> a </ci>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </list>  <list />  </list>  <apply>  <times />  <apply>  <power />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  <apply>  <power />  <cn type='integer'> 2 </cn>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <cn type='rational'> 1 <sep /> 2 </cn>  </apply>  </apply>  </apply>  <apply>  <ci> Inequality </ci>  <cn type='integer'> 0 </cn>  <lt />  <apply>  <arg />  <ci> z </ci>  </apply>  <leq />  <pi />  </apply>  </apply>  </annotation-xml>  </semantics>  </math> 
   
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  | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "a_"]], "2"], "-", "z_"]]], " ", RowBox[List["Gamma", "[", RowBox[List["a_", ",", RowBox[List["-", "z_"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Pi]", " ", "\[ImaginaryI]", " ", "a_"]], ")"]]]], "+", "z_"]]], " ", RowBox[List["Gamma", "[", RowBox[List["a_", ",", "z_"]], "]"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox["a", "2"], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", FractionBox["1", "2"], ",", FractionBox["a", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", FractionBox[SqrtBox[RowBox[List["-", SuperscriptBox["z", "2"]]]], "2"], ",", FractionBox["1", "2"]]], "]"]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]]]]], "/;", RowBox[List["0", "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]]]]]]]]  |  
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   Date Added to functions.wolfram.com (modification date)
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