4 papers
math.CA2020
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…
math.CA2020
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 …
math.CA2020
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…
math.CA2018
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 $…