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http://functions.wolfram.com/03.03.20.0013.02
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D[BesselY[\[Nu], z], {z, n}] == MeijerG[{{(1 - n)/2, -(n/2)},
{-((n + \[Nu] + 1)/2)}}, {{(\[Nu] - n)/2, -((\[Nu] + n)/2)},
{1/2, 0, -((n + \[Nu] + 1)/2)}}, z/2, 1/2] /;
Element[n, Integers] && n >= 0
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "n"]], "}"]]], RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "n"]], "2"], ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox[RowBox[List["n", "+", "\[Nu]", "+", "1"]], "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "n"]], "2"], ",", RowBox[List["-", FractionBox[RowBox[List["\[Nu]", "+", "n"]], "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "0", ",", RowBox[List["-", FractionBox[RowBox[List["n", "+", "\[Nu]", "+", "1"]], "2"]]]]], "}"]]]], "}"]], ",", FractionBox["z", "2"], ",", FractionBox["1", "2"]]], "]"]]]], "/;", 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> <mfrac> <mrow> <msup> <mo> ∂ </mo> <mi> n </mi> </msup> <mrow> <msub> <mi> Y </mi> <mi> ν </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <msup> <mi> z </mi> <mi> n </mi> </msup> </mrow> </mfrac> <mo> ⩵ </mo> <semantics> <mrow> <msubsup> <mi> G </mi> <mrow> <mn> 3 </mn> <mo> , </mo> <mn> 5 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> , </mo> <mn> 2 </mn> </mrow> </msubsup> <mo> ⁡ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> ❘ </mo> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> n </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mi> ν </mi> <mo> - </mo> <mi> n </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mi> ν </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> , </mo> <mn> 0 </mn> <mo> , </mo> <mrow> <mo> - </mo> <mfrac> <mrow> <mi> n </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "5"]], RowBox[List["2", ",", "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[TagBox[FractionBox["z", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]]]], MeijerG], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "n"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox["n", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox[RowBox[List["n", "+", "\[Nu]", "+", "1"]], "2"]]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[FractionBox[RowBox[List["\[Nu]", "-", "n"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox[RowBox[List["n", "+", "\[Nu]"]], "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["-", FractionBox[RowBox[List["n", "+", "\[Nu]", "+", "1"]], "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] </annotation> </semantics> </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> <partialdiff /> <bvar> <ci> z </ci> <degree> <ci> n </ci> </degree> </bvar> <apply> <ci> BesselY </ci> <ci> ν </ci> <ci> z </ci> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> n </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> n </ci> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> </list> <list> <list> <apply> <times /> <apply> <plus /> <ci> ν </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> n </ci> <ci> ν </ci> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> <list> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='integer'> 0 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> n </ci> <ci> ν </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </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[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "n_"]], "}"]]]]], RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "n"]], "2"], ",", RowBox[List["-", FractionBox["n", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["n", "+", "\[Nu]", "+", "1"]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["\[Nu]", "-", "n"]], "2"], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["\[Nu]", "+", "n"]], ")"]]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", "0", ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["n", "+", "\[Nu]", "+", "1"]], ")"]]]]]], "}"]]]], "}"]], ",", FractionBox["z", "2"], ",", FractionBox["1", "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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