9 citations · 76 across the 82 of their papers we have counts for
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A uniform asymptotic expansion for the incomplete gamma functions revisited
R B Paris
A new uniform asymptotic expansion for the incomplete gamma function valid for large values of was given by the author in {\it J. Comput. Appl. Math.} {\bf 148} (2002)…
Asymptotics of a Gauss hypergeometric function with large parameters, III: Application to the Legendre functions of large imaginary order and real degree
R. B. Paris
We obtain the asymptotic expansion for the Gauss hypergeometric function \[F(a-λ,b+λ;c+iαλ;z)\] for with , and finite parameters by application of…
Integrals of products of Hurwitz zeta functions via Feynman parametrization and two double sums of Riemann zeta functions
M. A. Shpot, R. B. Paris
We consider two integrals over involving products of the function , where is the Hurwitz zeta function, given by $$\int_0^1ζ_1(a…
The asymptotics of the Touchard polynomials: a uniform approximation
R B Paris
The asymptotic expansion of the Touchard polynomials (also known as the exponential polynomials) for large and complex values of the variable , where may be f…
The asymptotics of the Touchard polynomials
R B Paris
We examine the asymptotic expansion of the Touchard polynomials (also known as the exponential polynomials) for large and complex values of the variable . In our tr…
On the Wilker and Huygens-type inequalities
C. P Chen, R B Paris
Chen and Cheung [C.-P. Chen, W.-S. Cheung, Sharpness of Wilker and Huygens type inequalities, J. Inequal. Appl. 2012 (2012) 72, \url{http://dx.doi.org/10.1186/1029-242X-2012-72}] e…
The Stokes phenomenon and the Lerch zeta function
R B Paris
We examine the exponentially improved asymptotic expansion of the Lerch zeta function for large complex values of , with an…
Exponentially small expansions associated with a generalised Mathieu series
R B Paris
We consider the generalised Mathieu series \[\sum_{n=1}^\infty \frac{n^γ}{(n^λ+a^λ)^μ}\qquad (μ>0)\] when the parameters () and are even integers for large complex …
Some results associated with Bernoulli and Euler numbers with applications
C. -P. Chen, R. B. Paris
In this paper, we present series representations of the remainders in the expansions for , $\mbox{sech} t$ and . For example, we prove that for and $N\i…