If Lmn(x) is the Laguerre polynomial of order m and degree n
Is there a means of computing Lmn(x) for
1) m goes to infinity
2) n goes to infinity
Ganie Abdul Hamid
Popular answer
I may recommend here
https://math.stackexchange.com/questions/1797429/infinite-sum-involving-laguerre-polynomials
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Pinchas Malits
I recommend you to read :
Dan Dai, Mourad E.H.Ismail, Jun Wang. Asymptotics for Laguerre polynomials with large order and parameters. Journal of Approximation Theory 193 (2015) 4–19
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Maged Gumaan Bin-Saad
In fact, in quantum mechanics, we need the associated Laguerre polynomials L_{n}^{m}(x), where n in {0,1,2,3,...,\infty} and m>-1 according to the definition of the associated Laguerre polynomials.
L_{n}^{m}(x) are defined by
L_{n}^{m}(x)=(-1)^{k} D^{k}_{x} L_{n+k}(x) , that mean k goes not to infinity.
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