9 citations · 76 across the 82 of their papers we have counts for
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Exponentially small expansions related to the parabolic cylinder function
R B Paris
The refined asymptotic expansion of the confluent hypergeometric function on the Stokes line given in {\it Appl. Math. Sci.} {\bf 7} (2013) 6601--6609 is emp…
Asymptotic expansion of the modified exponential integral involving the Mittag-Leffler function
R B Paris
We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [{\it Fract. Calc. App…
Asymptotic expoansions of mathieu-Bessel series. I
R B Paris
We consider the asymptotic expansion of the Mathieu-Bessel series \[S_ν(a,b)=\sum_{n=1}^\infty \frac{n^γJ_ν(nb/a)}{(n^2+a^2)^μ}, \qquad (μ, b>0,\ γ, ν\in {\bf R})\] as $a\to+\infty…
High-order derivatives of the Bessel functions with an application
R B Paris
We determine the asymptotic behaviour of the th derivatives of the Bessel functions and , where is a fixed positive quantity, as . These results…
Asymptotics of a sum of modified Bessel functions with non-linear argument
R B Paris
We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \[S_{ν,p}(a)=\sum_{n\geq 1} (an^p/2)^{-ν} K_ν(an^p)\qquad (a>0,…
The evaluation of a weighted sum of Gauss hypergeometric functions and its connection with Galton-Watson processes
R B Paris, Vladimir V Vinogradov
We evaluate the sum of Gauss hypergeometric functions \[S(μ,c;x)=\sum_{k\geq 0} \bl(\frac{1-x}{1+μ}\br)^k\,{}_2F_1(\fs k+\fs, \fs k+1;c;x)\] for and positive paramete…