Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site ContributeEmail CommentsSign the Guestbook

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











NevilleThetaC






Mathematica Notation

Traditional Notation









Elliptic Functions > NevilleThetaC[z,m] > Differential equations > Partial differential equations





http://functions.wolfram.com/09.09.13.0002.01









  


  










Input Form





16 z m^2 (m^2 + 1) D[NevilleThetaC[z, m], {m, 2}] D[NevilleThetaC[z, m], z] + 4 z^2 m D[NevilleThetaC[z, m], z]^2 + 4 z m^2 D[NevilleThetaC[z, m], z, m] D[NevilleThetaC[z, m], {z, 2}] + (m - 1) NevilleThetaC[z, m]^2 - D[NevilleThetaC[z, m], {z, 2}]^2 + 2 (m - 1) D[NevilleThetaC[z, m], m] (2 z ((9 m - 5) D[NevilleThetaC[z, m], z] - 4 (m - 1) m D[NevilleThetaC[z, m], z, m]) + 5 D[NevilleThetaC[z, m], {z, 2}]) m - 24 (m - 1)^2 m^2 D[NevilleThetaC[z, m], m]^2 - 4 m^2 z^2 D[NevilleThetaC[z, m], z]^2 - 32 m^3 z D[NevilleThetaC[z, m], {m, 2}] D[NevilleThetaC[z, m], z] - 4 m z D[NevilleThetaC[z, m], z, m] D[NevilleThetaC[z, m], {z, 2}] + 2 (m - 1) NevilleThetaC[z, m] (D[NevilleThetaC[z, m], {z, 2}] + m (4 m D[NevilleThetaC[z, m], m] + 2 (m - 1) (2 m D[NevilleThetaC[z, m], {m, 2}] - z D[NevilleThetaC[z, m], z, m]) - D[NevilleThetaC[z, m], {z, 2}, m])) - 4 (m - 1) m z D[NevilleThetaC[z, m], z] D[NevilleThetaC[z, m], {z, 2}, m] == 0










Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["16", " ", "z", " ", SuperscriptBox["m", "2"], " ", RowBox[List["(", " ", RowBox[List[SuperscriptBox["m", "2"], "+", "1"]], ")"]], RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["m", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z", "2"], "m", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], "2"]]], "+", RowBox[List["4", " ", "z", " ", SuperscriptBox["m", "2"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z", ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]], "2"]]], "-", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], "2"], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", "m"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["9", " ", "m"]], "-", "5"]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", "m", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z", ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]], ")"]], " ", "m"]], "-", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], "2"], " ", SuperscriptBox["m", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", "m"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["m", "2"], " ", SuperscriptBox["z", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], ")"]], "2"]]], "-", RowBox[List["32", " ", SuperscriptBox["m", "3"], " ", "z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["m", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "-", RowBox[List["4", " ", "m", " ", "z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z", ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], "+", RowBox[List["m", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "m", " ", RowBox[List[SubscriptBox["\[PartialD]", "m"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["m", ",", "2"]], "}"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], "-", RowBox[List["z", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z", ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]], ")"]]]], "-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]], ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m", "-", "1"]], ")"]], " ", "m", " ", "z", " ", RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z", ",", "2"]], "}"]], ",", "m"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z", ",", "m"]], "]"]]]]]]]], "\[Equal]", "0"]]]]










MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 32 </mn> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 3 </mn> </msup> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mn> 24 </mn> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 16 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mi> m </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mtext> </mtext> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mtext> </mtext> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 5 </mn> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <mi> m </mi> </mrow> <mo> - </mo> <mn> 5 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 3 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> - </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> + </mo> <mrow> <mi> m </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mfrac> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> m </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> m </mi> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <mo> - </mo> <mrow> <mi> z </mi> <mo> &#8290; </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 2 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mo> &#8706; </mo> <mn> 3 </mn> </msup> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mo> &#8706; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> &#8290; </mo> <mtext> &#8201; </mtext> <mrow> <mo> &#8706; </mo> <mi> m </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <mi> &#977; </mi> <mi> c </mi> </msub> <mo> ( </mo> <mrow> <mi> z </mi> <mo> &#10072; </mo> <mi> m </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <plus /> <apply> <times /> <cn type='integer'> -32 </cn> <ci> z </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> 3 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16 </cn> <apply> <plus /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> m </ci> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> z </ci> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 5 </cn> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 9 </cn> <ci> m </ci> </apply> <cn type='integer'> -5 </cn> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> <apply> <times /> <ci> m </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> m </ci> <apply> <partialdiff /> <bvar> <ci> m </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <partialdiff /> <bvar> <ci> z </ci> <degree> <cn type='integer'> 2 </cn> </degree> </bvar> <bvar> <ci> m </ci> </bvar> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <ci> NevilleThetaC </ci> <ci> z </ci> <ci> m </ci> </apply> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["16", " ", "z_", " ", SuperscriptBox["m_", "2"], " ", RowBox[List["(", RowBox[List[SuperscriptBox["m_", "2"], "+", "1"]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["m_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List["4", " ", SuperscriptBox["z_", "2"], " ", "m_", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], ")"]], "2"]]], "+", RowBox[List["4", " ", "z_", " ", SuperscriptBox["m_", "2"], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_", ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", SuperscriptBox[RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]], "2"]]], "-", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], ")"]], "2"], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "z_", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["9", " ", "m_"]], "-", "5"]], ")"]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", "m_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_", ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]]]], ")"]]]], "+", RowBox[List["5", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]]]], ")"]], " ", "m_"]], "-", RowBox[List["24", " ", SuperscriptBox[RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], "2"], " ", SuperscriptBox["m_", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], ")"]], "2"]]], "-", RowBox[List["4", " ", SuperscriptBox["m_", "2"], " ", SuperscriptBox["z_", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], ")"]], "2"]]], "-", RowBox[List["32", " ", SuperscriptBox["m_", "3"], " ", "z_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["m_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "-", RowBox[List["4", " ", "m_", " ", "z_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_", ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], "+", RowBox[List["m_", " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "m_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "m_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["m_", ",", "2"]], "}"]]]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], "-", RowBox[List["z_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_", ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]]]], ")"]]]], "-", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]], ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["4", " ", RowBox[List["(", RowBox[List["m_", "-", "1"]], ")"]], " ", "m_", " ", "z_", " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]], " ", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "2"]], "}"]], ",", "m_"]]], RowBox[List["NevilleThetaC", "[", RowBox[List["z_", ",", "m_"]], "]"]]]]]]]], "]"]], "\[RuleDelayed]", "0"]]]]










Date Added to functions.wolfram.com (modification date)





2001-10-29





© 1998-2014 Wolfram Research, Inc.