LaguerreL[4, \[Lambda], z] == (1/24) (z^4 - 4 z^3 (4 + \[Lambda]) + 6 z^2 (12 + 7 \[Lambda] + \[Lambda]^2) - 4 z (24 + 26 \[Lambda] + 9 \[Lambda]^2 + \[Lambda]^3) + 24 + 50 \[Lambda] + 35 \[Lambda]^2 + 10 \[Lambda]^3 + \[Lambda]^4)

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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> <msubsup> <mi> L </mi> <mn> 4 </mn> <mi> &#955; </mi> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 24 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 4 </mn> </msup> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> &#955; </mi> <mo> + </mo> <mn> 4 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 6 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 12 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> <mo> + </mo> <mrow> <mn> 9 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 26 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> + </mo> <msup> <mi> &#955; </mi> <mn> 4 </mn> </msup> <mo> + </mo> <mrow> <mn> 10 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35 </mn> <mo> &#8290; </mo> <msup> <mi> &#955; </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 50 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> <mo> + </mo> <mn> 24 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> LaguerreL </ci> <cn type='integer'> 4 </cn> <ci> &#955; </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 24 </cn> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 12 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 26 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 24 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <times /> <cn type='integer'> 10 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 35 </cn> <apply> <power /> <ci> &#955; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 50 </cn> <ci> &#955; </ci> </apply> <cn type='integer'> 24 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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2001-10-29