Stokes phenomena in classical special functions - Bessel and Weber functions with applications

The concept of asymptotic expansion for complex functions in one variable is well established and widely used since Poincar´ e, in order to give a meaning to divergent formal

Carleson’s celebrated theorem of 1965 [14] asserts the pointwise convergence of the partial Fourier sums of square integrable functions.. We give a proof of this fact, in particular

The Dwellers in the Garden of Allah 109... The Dwellers in the Garden of Allah

In practice, the most used techniques to derive analytic expansions are based on local approximations that are either convergent (Taylor series) or divergent (asymptotic ex-

The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu- ous

The strong variants of continuity with which we shall be dealing in this paper include strongly continuous functions introduced by Levine [13], perfectly continuous functions

This expansion has the additional property of being asymptotic for large c with fixed a uniformly in b and z (with bounded b/c).. Moreover, the asymptotic character of the

Toeplitz determinants with special rational generating functions may be evaluated in terms of the double gamma function and the Gauss hypergeometric function [5].. Several properties