I have found that associated Laguerre polynomials can be expressed in terms of spherical Bessel function ($j_n$, $y_n$) but what about in terms of Bessel functions of the first kind ($J_a$)?
The relevant formulas I have found which connect these two include limits and integrals, f.e.1, 2 and 3 which denote asymptotic behaviour of associated Laguerre polynomials to the Bessel functions of first kind under some provisions.
Does anyone know a more linear relation?
(The problem is of relevance to atomic hydrogen orbitals and Chladni figures. Such a straightforward linear relation would be a good explanation, I believe, of why some Chlani figures resemble to projections of the said orbitals. Any comment on this one is also welcome).