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http://functions.wolfram.com/06.07.26.0007.01
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Gamma[a, 0, Sqrt[z]] == (2^(a - 1)/Sqrt[Pi])
MeijerG[{{1}, {}}, {{a/2, (a + 1)/2}, {0}}, z/4]
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Cell[BoxData[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["a", ",", "0", ",", SqrtBox["z"]]], "]"]], "\[Equal]", RowBox[List[FractionBox[SuperscriptBox["2", RowBox[List["a", "-", "1"]]], SqrtBox["\[Pi]"]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["a", "2"], ",", FractionBox[RowBox[List["a", "+", "1"]], "2"]]], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", FractionBox["z", "4"]]], "]"]]]]]]]]
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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> <mi> Γ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msup> <mn> 2 </mn> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <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> 2 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> </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["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox["z", "4"], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox["1", MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[FractionBox["a", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "1"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mi> Γ </mi> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <msup> <mn> 2 </mn> <mrow> <mi> a </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <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> 2 </mn> <mo> , </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mn> 1 </mn> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mi> a </mi> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> </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["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[FractionBox["z", "4"], MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox["1", MeijerG, Rule[Editable, True]]], List[RowBox[List[TagBox[FractionBox["a", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "1"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </mrow> </mrow> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List["a_", ",", "0", ",", SqrtBox["z_"]]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["a", "-", "1"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "1", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["a", "2"], ",", FractionBox[RowBox[List["a", "+", "1"]], "2"]]], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", FractionBox["z", "4"]]], "]"]]]], SqrtBox["\[Pi]"]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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