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
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.