MHB Relation between Hermite and associated Laguerre

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The discussion focuses on proving the relationship between Hermite polynomials and associated Laguerre polynomials, specifically the expression H_{2n}(x)=(-1)^n2^{2n}n!L_n^{-\frac{1}{2}}(x^2). Participants emphasize the importance of demonstrating prior effort or thoughts on the problem before seeking assistance. If a participant is unsure how to start, they are encouraged to request a hint instead of a complete solution. The community values efficient use of time and knowledge sharing. Overall, the thread highlights the collaborative nature of mathematical problem-solving.
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Please help me in proving the following expression

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

where $$H_n$$ is the Hermite polynomial and $$L_n^{-\frac{1}{2}}$$ is the associated Laguerre polynomial.
 
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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.
 

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