9 citations · 76 across the 82 of their papers we have counts for
82 papers
On the -zeros of the Bessel functions of purely imaginary order
R B Paris
The -zeros of the Bessel functions of purely imaginary order are examined for fixed argument . In the case of the modified Bessel function of the second kind , i…
An asymptotic approximation for the Riemann zeta function revisited
R B Paris
We revisit a representation for the Riemann zeta function expressed in terms of normalised incomplete gamma functions given by the author and S. Cang in Methods Appl. Anal.…
The asymptotic expansion of the Humbert hyper-Bessel function
R B Paris
We consider the asymptotic expansion of the Humbert hyper-Bessel function expressed in terms of a hypergeometric function by \[J_{m,n}(x)=\frac{(x/3)^{m+n}}{m! n!}\,{}_0F…
An extension of an asymptotic result of Tricomi concerning a definite integral
R B Paris
We consider the expansion of an integral considered by F.G. Tricomi given by \[\int_{-\infty}^\infty x e^{-x^2}(\frac{1}{2}+\frac{1}{2}\mbox{erf}\,x)^{m} dx\] as . The…
The asymptotic expansion of Kratzel's integral and an integral related to an extension of the Whittaker function
R B Paris
We consider the asymptotic expansion of Krätzel's integral \[F_{p,ν}(x)=\int_0^\infty t^{ν-1} e^{-t^p-x/t}\,dt\qquad (|\arg\,x|<π/2),\] for as in the sector $…
The asymptotic expansion of a Mathieu-exponential series
R B Paris
We consider the asymptotic expansion of the functional series \[S_μ^\pm(a;λ)=\sum_{n=0}^\infty \frac{(\pm 1)^n e^{-λn}}{(n^2+a^2)^μ}\] for and as in…