9 citations · 76 across the 82 of their papers we have counts for
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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…
Asymptotic expansion of the Wright function for large variable and parameter
R B Paris
We consider the asymptotic expansion of the Wright function \[W_{λ,μ}(z)=\sum_{n=0}^\infty\frac{z^n}{n! Γ(λn+μ)}\qquad (λ>-1)\] for large (positive and negative) variable and large…
The asymptotic expansion of the Bateman and Havelock functions of large order and argument
R B Paris
Asymptotic expansions for the Bateman and Havelock functions defined respectively by the integrals \[\frac{2}π\int_0^{π/2} \!\!\!\begin{array}{c} \cos\\\sin\end{array}\!(x\tan u-νu…
On the -zeros of the modified Bessel function of positive argument
R B Paris
The modified Bessel function of the second kind of imaginary order for fixed possesses a countably infinite sequence of real zeros. Recently it has been shown tha…
The numerical evaluation of the Riesz function
R B Paris
The behaviour of the generalised Riesz function defined by \[S_{m,p}(x)=\sum_{k=0}^\infty \frac{(-)^{k-1}x^k}{k! ζ(mk+p)}\qquad (m\geq 1,\ p\geq 1)\] is considered for large positi…