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http://functions.wolfram.com/06.07.06.0010.01
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Gamma[n, Subscript[z, 1], Subscript[z, 2]] \[Proportional]
(Subscript[z, 2]^n - Subscript[z, 1]^n)/n + O[Subscript[z, 1]^(n + 1)] +
O[Subscript[z, 2]^(n + 1)] /; Element[n, Integers] && n > 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["n", ",", SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["z", "2", "n"], "-", SubsuperscriptBox["z", "1", "n"]]], "n"], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "1", RowBox[List["n", "+", "1"]]], "]"]], "+", RowBox[List["O", "[", SubsuperscriptBox["z", "2", RowBox[List["n", "+", "1"]]], "]"]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "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> <mi> n </mi> <mo> , </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mo> , </mo> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mrow> <mo> ) </mo> </mrow> <mo> ∝ </mo> <mrow> <mfrac> <mrow> <msubsup> <mi> z </mi> <mn> 2 </mn> <mi> n </mi> </msubsup> <mo> - </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mi> n </mi> </msubsup> </mrow> <mi> n </mi> </mfrac> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 1 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ) </mo> </mrow> <mo> + </mo> <mrow> <mi> O </mi> <mo> ⁡ </mo> <mo> ( </mo> <msubsup> <mi> z </mi> <mn> 2 </mn> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> n </mi> <mo> ∈ </mo> <msup> <mi> ℕ </mi> <mo> + </mo> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <ci> Proportional </ci> <apply> <ci> Gamma </ci> <ci> n </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <ci> n </ci> </apply> </apply> </apply> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <apply> <ci> O </ci> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <apply> <ci> SuperPlus </ci> <ci> ℕ </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Gamma", "[", RowBox[List["n_", ",", SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[SubsuperscriptBox["zz", "2", "n"], "-", SubsuperscriptBox["zz", "1", "n"]]], "n"], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "1"], "]"]], RowBox[List["n", "+", "1"]]], "+", SuperscriptBox[RowBox[List["O", "[", SubscriptBox["zz", "2"], "]"]], RowBox[List["n", "+", "1"]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "0"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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