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http://functions.wolfram.com/06.05.03.0012.01
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Gamma[2/3 - n] == (((-1)^n 3^n)/Product[3 k - 2, {k, 1, n}]) Gamma[2/3] /;
Element[n, Integers] && n >= 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["2", "3"], "-", "n"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["3", "n"], " "]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["(", RowBox[List[RowBox[List["3", " ", "k"]], "-", "2"]], ")"]]]]], RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]
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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> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> - </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> ⁢ </mo> <msup> <mn> 3 </mn> <mi> n </mi> </msup> </mrow> <mrow> <munderover> <mo> ∏ </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mi> n </mi> </munderover> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mfrac> <mn> 2 </mn> <mn> 3 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <mi> ℕ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> Gamma </ci> <apply> <plus /> <cn type='rational'> 2 <sep /> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> <apply> <power /> <cn type='integer'> 3 </cn> <ci> n </ci> </apply> <apply> <power /> <apply> <product /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 1 </cn> </lowlimit> <uplimit> <ci> n </ci> </uplimit> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> k </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> ℕ </ci> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List[FractionBox["2", "3"], "-", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", SuperscriptBox["3", "n"]]], ")"]], " ", RowBox[List["Gamma", "[", FractionBox["2", "3"], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["k", "=", "1"]], "n"], RowBox[List["(", RowBox[List[RowBox[List["3", " ", "k"]], "-", "2"]], ")"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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