D[BesselY[\[Nu], z], z] == 0 /; z == Subscript[z, k] && Element[k, Integers] && k >= 0 && Element[\[Nu], Reals] && Re[Subscript[z, k]] == Subscript[z, k]

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["BesselY", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["z", "\[Equal]", SubscriptBox["z", "k"]]], "\[And]", RowBox[List["k", "\[Element]", "Integers"]], "\[And]", RowBox[List["k", "\[GreaterEqual]", "0"]], "\[And]", RowBox[List["\[Nu]", "\[Element]", "Reals"]], "\[And]", RowBox[List[RowBox[List["Re", "[", SubscriptBox["z", "k"], "]"]], "\[Equal]", SubscriptBox["z", "k"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> Y </mi> <mi> &#957; </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> z </mi> <mo> &#10869; </mo> <msub> <mi> z </mi> <mi> k </mi> </msub> </mrow> <mo> &#8743; </mo> <mrow> <mi> k </mi> <mo> &#8712; </mo> <semantics> <mi> &#8469; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalN]&quot;, Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> &#957; </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mi> Re </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <msub> <mi> z </mi> <mi> k </mi> </msub> <mo> ) </mo> </mrow> </mrow> <mo> &#10869; </mo> <msub> <mi> z </mi> <mi> k </mi> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> BesselY </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <and /> <apply> <eq /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> k </ci> </apply> </apply> <apply> <in /> <ci> k </ci> <integers /> </apply> <apply> <in /> <ci> &#957; </ci> <reals /> </apply> <apply> <eq /> <apply> <times /> <real /> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> k </ci> </apply> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <ci> k </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["BesselY", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["z", "\[Equal]", SubscriptBox["z", "k"]]], "&&", RowBox[List["k", "\[Element]", "Integers"]], "&&", RowBox[List["k", "\[GreaterEqual]", "0"]], "&&", RowBox[List["\[Nu]", "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["Re", "[", SubscriptBox["z", "k"], "]"]], "\[Equal]", SubscriptBox["z", "k"]]]]]]]]]]]

2001-10-29