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 | | http://functions.wolfram.com/01.15.13.0002.01 | 
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 | | (Subscript[z, 1]^2 + Subscript[z, 2]^2) 
    D[w[Subscript[z, 1], Subscript[z, 2]], Subscript[z, 2], 
     Subscript[z, 2]] + 2 Subscript[z, 2] 
    D[w[Subscript[z, 1], Subscript[z, 2]], Subscript[z, 2]] == 0 /; 
 w[Subscript[z, 1], Subscript[z, 2]] == ArcTan[Subscript[z, 1], 
   Subscript[z, 2]] | 
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 | | Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["z", "1", "2"], "+", SubsuperscriptBox["z", "2", "2"]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["z", "2"], ",", SubscriptBox["z", "2"]]]], RowBox[List["w", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]]]]], "+", RowBox[List["2", " ", SubscriptBox["z", "2"], " ", RowBox[List[SubscriptBox["\[PartialD]", SubscriptBox["z", "2"]], RowBox[List["w", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]]]]]]], "\[Equal]", "0"]], "/;", RowBox[List[RowBox[List["w", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List["ArcTan", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]]]]]]] | 
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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>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <msubsup>  <mi> z </mi>  <mn> 1 </mn>  <mn> 2 </mn>  </msubsup>  <mo> + </mo>  <msubsup>  <mi> z </mi>  <mn> 2 </mn>  <mn> 2 </mn>  </msubsup>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mfrac>  <mrow>  <msup>  <mo> ∂ </mo>  <mn> 2 </mn>  </msup>  <mrow>  <mi> w </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msub>  <mi> z </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mo> ∂ </mo>  <msubsup>  <mi> z </mi>  <mn> 2 </mn>  <mn> 2 </mn>  </msubsup>  </mrow>  </mfrac>  </mrow>  <mtext>   </mtext>  <mo> + </mo>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <mfrac>  <mrow>  <mo> ∂ </mo>  <mrow>  <mi> w </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <msub>  <mi> z </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mrow>  <mo> ∂ </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  </mfrac>  <mo> ⁢ </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mn> 0 </mn>  </mrow>  <mo> /; </mo>  <mrow>  <mrow>  <mi> w </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <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>  <msup>  <mi> tan </mi>  <mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  </msup>  <mo> ( </mo>  <mrow>  <msub>  <mi> z </mi>  <mn> 1 </mn>  </msub>  <mo> , </mo>  <msub>  <mi> z </mi>  <mn> 2 </mn>  </msub>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <ci> Condition </ci>  <apply>  <eq />  <apply>  <plus />  <apply>  <times />  <apply>  <plus />  <apply>  <power />  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 1 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <ci> D </ci>  <apply>  <ci> w </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>  <list>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <cn type='integer'> 2 </cn>  </list>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <ci> D </ci>  <apply>  <ci> w </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>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <ci> Subscript </ci>  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  </apply>  <cn type='integer'> 0 </cn>  </apply>  <apply>  <eq />  <apply>  <ci> w </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>  <arctan />  <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>  </apply>  </annotation-xml>  </semantics>  </math> 
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 | | Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SubsuperscriptBox["z_", "1", "2"], "+", SubsuperscriptBox["z_", "2", "2"]]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["z_", "2"], ",", SubscriptBox["z_", "2"]]]], RowBox[List["w", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]]]]]], "+", RowBox[List["2", " ", SubscriptBox["z_", "2"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[SubscriptBox["z_", "2"]]]], RowBox[List["w", "[", RowBox[List[SubscriptBox["z_", "1"], ",", SubscriptBox["z_", "2"]]], "]"]]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[RowBox[List["w", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]], "\[Equal]", RowBox[List["ArcTan", "[", RowBox[List[SubscriptBox["z", "1"], ",", SubscriptBox["z", "2"]]], "]"]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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