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variants of this functions
LaguerreL






Mathematica Notation

Traditional Notation









Polynomials > LaguerreL[n,lambda,z] > Identities > Recurrence identities > Distant neighbors > With respect to lambda





http://functions.wolfram.com/05.08.17.0015.01









  


  










Input Form





LaguerreL[n, \[Lambda], z] == Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] LaguerreL[n, \[Lambda] - m, z] - ((-m + \[Lambda] + n)/z) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] LaguerreL[n, \[Lambda] - m - 1, z] /; Subscript[\[ScriptCapitalC], 0][n, \[Lambda], z] == 1 && Subscript[\[ScriptCapitalC], 1][n, \[Lambda], z] == (z + \[Lambda] - 1)/z && Subscript[\[ScriptCapitalC], m][n, \[Lambda], z] == ((-m + z + \[Lambda])/z) Subscript[\[ScriptCapitalC], m - 1][n, \[Lambda], z] - ((1 - m + \[Lambda] + n)/z) Subscript[\[ScriptCapitalC], m - 2][n, \[Lambda], z] && Element[m, Integers] && m > 0










Standard Form





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MathML Form







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</ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <ci> &#955; </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <ci> Subscript </ci> <ci> &#119966; </ci> <apply> <plus /> <ci> m </ci> <cn type='integer'> -2 </cn> </apply> </apply> <ci> n </ci> <ci> &#955; </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <apply> <ci> SuperPlus </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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