Luigi Gatteschi's work on asymptotics of special functions and their zeros
In the present article, L. Gatteschi's work on asymptotics of special functions (Jacobi, Laguerre, Hermite polynomials; Bessel functions of the first and second kind; Airy functions; confluent hypergeometric functions etc.) and their zeros is reviewed ``along methodological lines''. Many papers of L. Gatteschi (1923--2007) appeared in Italian journals and are sometimes difficult to obtain, so that the work of the present authors is beneficial in many ways. Major tools appearing in Gatteschi's work are the quantitative use of a method of Tricomi for deriving the asymptotics of zeros of functions from the asymptotics of the functions themselves (with explicit error bounds), Van der Corput's theory of ``enveloping series'', methods based on linear second-order differential equations and uniform expansions. The survey puts Gatteschi's work very well in the historical context of the development of the field of asymptotics of special functions, it highlights Gatteschi's major results and ends with an extensive bibliographic list.
scientific article; zbMATH DE number 5549492
scientific article