Strong asymptotics for Laguerre polynomials with varying weights

Abstract Supplementing and extending classical and recent results strong asymptotics for the Laguerre polynomials L n ( α n ) are established, as n → ∞, when the parameter α n depends on the degree n suitably. A case of particular interest is the one for which α n grows faster than n . Rescaling the argument z appropriately the resulting asymptotic forms are described by elementary functions, thereby extending the classical formulae of Plancherel-Rotach type for Laguerre polynomials L n ( α ) ( z ), α being fixed.

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