8 citations · 18 across the 18 of their papers we have counts for
18 papers
An expansion for the sum of a product of an exponential and a Bessel function. II
R B Paris
We examine the sum of a decaying exponential (depending non-linearly on the summation index) and a Bessel function in the form \[\sum_{n=1}^\infty e^{-an^p}\frac{J_ν(an^px)}{(an^px…
Some analytical results associated with extensions of the canonical Feller-Spitzer distribution
R. B. Paris, V. V. Vinogradov
In this work, we establish new analytical results which are required for the derivation of subtle properties of the members of two classes of the generalized Feller--Spitzer distri…
Refined asymptotics of the Riemann-Siegel theta function
R. B. Paris
The Riemann-Siegel theta function is examined for . Use of the refined asymptotic expansion for $\log\,\g(z)$ shows that the expansion of …
Uniform asymptotics of a Gauss hypergeometric function with two large parameters, V
R. B. Paris
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+ελ,b;c+λ;x),\qquad 0<x<1\] as in the neigbourhood of when the pa…
Asymptotic expansion of Mathieu-Bessel series. II
R B Paris
We consider the asymptotic expansion of the Mathieu-Bessel series \[S_{ν,γ}^μ(a,b)=\sum_{n=1}^\infty \frac{n^γK_ν(nb/a)}{(n^2+a^2)^μ}, \qquad (μ>0, ν\geq 0, b>0, γ\in {\bf R})\] as…
An asymptotic expansion for the error term in the Brent-McMillan algorithm for Euler's constant
R B Paris
The Brent-McMillan algorithm is the fastest known procedure for the high-precision computation of Euler's constant and is based on the modified Bessel functions and $…
Integrals of products of Hurwitz zeta functions and the Casimir effect in field theories
M. A. Shpot, M. P. Chaudhary, R. B. Paris
We evaluate two integrals over involving products of the function for , where is the Hurwitz zeta function. The eval…
Series representations of the remainders in the expansion for certain trigonometric and hyperbolic functions with applications
C. -P. Chen, R. B. Paris
In this paper, we present series representations of the remainders in the expansions for certain trigonometric and hyperbolic functions. By using the obtained results, we establish…
An asymptotic expansion for the Stieltjes constants
R. B. Paris
The Stieltjes constants appear in the coefficients in the Laurent expansion of the Riemann zeta function about the simple pole . We present an asymptotic expansio…
A derivation of two quadratic transformations contiguous to that of Gauss via a differential equation approach
M Swathi, A K Rathie, R B Paris
The purpose of this note is to provide an alternative proof of two quadratic transformation formulas contiguous to that of Gauss using a differential equation approach.
The expansion of a finite number of terms of the Gauss hypergeometric function of unit argument and the Landau constants
R. B. Paris
We obtain convergent inverse factorial expansions for the sum of the first terms of the Gauss hypergeometric function of unit argument valid for . The for…
On the asymptotics of a sequence of lacunary binomial-type polynomials
R. B. Paris
We examine the asymptotics of a sequence of lacunary binomial-type polynomials as that have arisen in the problem of the expected number of independ…
Exponential asymptotics of the Voigt functions
R B Paris
We obtain the asymptotic expansion of the Voigt functions and for large (real) values of the variables and , paying particular attention to the exponential…
An asymptotic expansion for the generalised quadratic Gauss sum revisited
R B Paris
An asymptotic expansion for the generalised quadratic Gauss sum where , are real and is a positive integer, is obtained…
On extensions of two results due to Ramanujan
Y. S. Kim, A. K. Rathie, R. B. Paris
The aim in this note is to provide a generalization of an interesting entry in Ramanujan's Notebooks that relate sums involving the derivatives of a function Phi(t) evaluated at 0…
An alternative proof of the extended Saalschutz summation theorem for the r+3Fr+2(1) series with applications
Y. S. Kim, Arjun K. Rathie, R. B. Paris
A simple proof of a new summation formula for a terminating r+3Fr+2(1) hypergeometric series, representing an extension of Saalschutz's formula for a 3F2(1) series, is given for t…
A note on a series containing the Laguerre polynomials
Y. S. Kim, A. K. Rathie, R. B. Paris
Expressions for the summation of a new series involving the Laguerre polynomials are obtained in terms of generalized hypergeometric functions. These results provide alternative, a…
On two Thomae-type transformations for hypergeometric series with integral parameter differences
Y. S. Kim, Arjun. K. Rathie, R. B. Paris
We obtain two new Thomae-type transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved…