Asymptotics of basic Bessel functions and \(q\)-Laguerre polynomials
Two asymptotic expansions for large values of the degree and order respectively are deduced for the \(q\)-Laguerre polynomial and the second Jackson \(q\)-Bessel function. The proof depend to a large extent on the \(q\)-binomial theorem and the elementary manipulation of series. A new proof is given of a theorem by \textit{J. E. Littlewood} [Proc. Lond. Math. Soc. 5, 361-410 (1907)] which proves to be very useful in the discussion of the asymptotic behaviour of \(q\)-functions in general. This study was partly motivated by the quantum study of disordered electronic systems.
scientific article; zbMATH DE number 739557