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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Differentiation > Low-order differentiation > With respect to z





http://functions.wolfram.com/05.08.20.0008.01









  


  








Input Form





D[(z^\[Lambda] LaguerreL[n, \[Lambda], z])/E^z, z] == ((n + 1) z^(\[Lambda] - 1) LaguerreL[n + 1, \[Lambda] - 1, z])/E^z








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "z"], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], SuperscriptBox["z", "\[Lambda]"], RowBox[List["LaguerreL", "[", RowBox[List["n", ",", "\[Lambda]", ",", "z"]], "]"]]]], ")"]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], SuperscriptBox["z", RowBox[List["\[Lambda]", "-", "1"]]], RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <mrow> <mo> &#8706; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> &#955; </mi> </msup> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> &#8706; </mo> <mi> z </mi> </mrow> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> &#955; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msubsup> <mi> L </mi> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mi> &#955; </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <partialdiff /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#955; </ci> </apply> <apply> <ci> LaguerreL </ci> <ci> n </ci> <ci> &#955; </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> LaguerreL </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> -1 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["z_"]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z_"]]], " ", SuperscriptBox["z_", "\[Lambda]_"], " ", RowBox[List["LaguerreL", "[", RowBox[List["n_", ",", "\[Lambda]_", ",", "z_"]], "]"]]]], ")"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["(", RowBox[List["n", "+", "1"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], " ", SuperscriptBox["z", RowBox[List["\[Lambda]", "-", "1"]]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["n", "+", "1"]], ",", RowBox[List["\[Lambda]", "-", "1"]], ",", "z"]], "]"]]]]]]]]


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





2001-10-29