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Relation between Hermite and associated Laguerre

suvadip

Member
Feb 21, 2013
69
Please help me in proving the following expression

\(\displaystyle H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2)\)

where \(\displaystyle H_n\) is the Hermite polynomial and \(\displaystyle L_n^{-\frac{1}{2}}\) is the associated Laguerre polynomial.
 
Last edited by a moderator:

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Hello suvadip,

By now you should know we expect some effort to be given, such as the work you have tried, or the thoughts you have on how to proceed, for the reasons I have already given. You may already have tried something, and one of our helpers may give you information you already know, and this would be a waste of the helper's time, which is valuable.

If you simply have no idea how to begin, then you should state this, and ask for a hint to begin.