9 citations · 76 across the 82 of their papers we have counts for
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An asymptotic expansion for a sum of modified Bessel functions with quadratic argument
R. B. Paris
We examine the sum of modified Bessel functions with argument depending quadratically on the summation index given by \[S_ν(a)=\sum_{n\geq 1} (\frac{1}{2} an^2)^{-ν} K_ν(an^2)\qqua…
Asymptotics of a Gauss hypergeometric function with large parameters, IV: A uniform expansion
R B Paris
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[F(a+ελ,m;c+λ;x),\qquad λ\to+\infty\] for and positive integer when the parameter $ε>1…
Asymptotics of a hypergeometric function with four large parameters
R B Paris
We consider the asymptotic behaviour of the generalised hypergeometric function \[{}_3F_2\bl(\!\!\begin{array}{c} 1, (1+t)k/2, (1+t)k/2+1/2\\tk+1, k+1\end{array}\!\!; x\br),\qquad…
A note on an integral of Dixit, Roy and Zaharescu
R B Paris
In a recent paper, Dixit {\it et al.\/} [Acta Arith. {\bf 177} (2017) 1--37] posed two open questions whether the integral \[{\hat J}_{k}(α)=\int_0^\infty\frac{xe^{-αx^2}}{e^{2πx}-…
The evaluation of infinite sums of products of Bessel functions
R B Paris
We examine convergent representations for the sum of Bessel functions \[\sum_{n=1}^\infty \frac{J_μ(na) J_ν(nb)}{n^α}\] for , and positive values of and . Such r…
A summation formula for a hypergeometric series
R B Paris
A summation formula is derived for the hypergeometric series of unit argument , where and .