Now showing items 1-10 of 20
The asymptotics of the generalised Hermite–Bell polynomials
The Hermite–Bell polynomials are defined by [formula missing] for n=0,1,2,… and integer r≥2 and generalise the classical Hermite polynomials corresponding to r=2. We obtain an asymptotic expansion for [formula missing] as ...
Asymptotics of the Gauss hypergeometric function with large parameters, II
(Element d.o.o., 2013)
We obtain asymptotic expansions by application of the method of steepest descents for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+λ;z) as |λ| → ∞ when 0<ε1 <1 and ε1 >1 where, without loss of generality, it is supposed ...
Asymptotics of the Gauss hypergeometric function with large parameters, I
(Element d.o.o., 2013)
We obtain asymptotic expansions for the Gauss hypergeometric function F(a+ε1λ,b+ε2λ;c+ε3λ;z) as |λ| →∞ when the εj are ﬁnite by an application of the method of steepest descents, thereby extending previous results corresponding ...
Inequalities, asymptotic expansions and completely monotonic functions related to the gamma function
In this paper, we present some completely monotonic functions and asymptotic expansions related to the gamma function. Based on the obtained expansions, we provide new bounds for Γ(x + 1)/Γ(x + 1/2) and Γ(x + 1/2).
Asymptotics of integrals of Hermite polynomials
(Hikari Ltd, 2010)
Integrals involving products of Hermite polynomials with the weight factor exp (−x2) over the interval (−∞,∞) are considered. A result of Azor, Gillis and Victor (SIAM J. Math. Anal. 13 (1982) 879–890] is derived by ...
Asymptotic expansion of n-dimensional Faxén-type integrals
(European Journal of Pure and Applied Mathematics (EJPAM), 2010)
The asymptotic expansion of n-dimensional extensions of Faxén’s integral In(z) are derived for large complex values of the variable z. The theory relies on the asymptotics of the generalised hypergeometric, orWright, ...
The discrete analogue of Laplace’s method
We give a justification of the discrete analogue of Laplace’s method applied to the asymptotic estimation of sums consisting of positive terms. The case considered is the series related to the hypergeometric function ...
The asymptotics of the mittag-leffler polynomials
(Element d.o.o., 2012)
We investigate the asymptotic behaviour of the Mittag-Leffler polynomials Gn(z) for large n and z, where z is a complex variable satisfying 0 arg z 12 π . A summary of the asymptotic properties of Gn(ix) for real ...
On the asymptotic expansion of a binomial sum involving powers of the summation index
(Element d.o.o., 2012-10)
Asymptotic approximations for n!
Several approximations for n! have recently appeared in the literature. We show here how these approximations can be derived by expansion of certain polynomials in inverse powers of n and comparison with Stirling’s asymptotic ...