Olde Daalhuis,

Asymptotic expansions of q-gamma, q-exponential and q-bessel functions, Journal of Mathematical Analysis and Applications, 186 (1994), 896-913.

2004), by giving complete

asymptotic expansions in terms of the Airy function.

Using the concepts of a neutrix and neutrix limit, the first author gave a general principle for the discarding of unwanted infinite quantities from

asymptotic expansions, and this has been exploited particularly in connection with multiplication, convolution and composition of distributions, see [4,5].

The main purpose of this paper is to obtain the first term in the

asymptotic expansions of [[phi].

Asymptotic expansions and analytic continuations of the H-function have been discussed by Braaksma ((1)).

In the context of computing

asymptotic expansions of sums and series, usually the most useful form of the Euler-Maclaurin formula is

4), we use the ideas from [6,10] of

asymptotic expansions of the Bessel functions.

The researchers develop solutions to the Korteweg-de Vries and Camassa-Holm equation,

asymptotic expansions for the partial sums of the exponential series, and two parameter deformations of Chebyshev polynomials with simple recurrence coefficients.

As a matter of fact, the

asymptotic expansions of many special functions are divergent.

In this paper, we first derive

asymptotic expansions concerning the preconditioned matrices [P.

In Section 4 we investigate a similar modification applied to uniform

asymptotic expansions, and we present the function [K.

In particular, the asymptotic analysis of the above integral is amenable for the saddle-point method to obtain uniform

asymptotic expansions for the coefficients in (4) for ([n.