9 citations · 19 across the 16 of their papers we have counts for
16 papers
A note on an integral associated with the Kelvin ship-wave pattern
R. B. Paris
The velocity potential in the Kelvin ship-wave source can be partly expressed in terms of space derivatives of the single integral \[F(x,ρ,α)=\int_{-\infty}^\infty \exp\,[-\frac{1}…
On an extension of Watson's lemma due to Ursell
R. B. Paris
In 1991, Ursell gave a strong form of Watson's lemma for the Laplace integral \[\int_0^\infty e^{-xt}f(t)\,dt\qquad (x\rightarrow+\infty) \] in which the amplitude function …
A note on a class of exact solutions for a doubly anharmonic oscillator
R. B. Paris
We examine a class of exact solutions for the eigenvalues and eigenfunctions of a doubly anharmonic oscillator defined by the potential , . These…
The asymptotic expansion of a generalisation of the Euler-Jacobi series
R. B. Paris
We consider the asymptotic expansion of the sum \[S_p(a;w)=\sum_{n=1}^\infty n^{-w}\e^{-an^p}\] as in for arbitrary finite and . Our atte…
The asymptotics of a generalised Beta function
R. B. Paris
We consider the generalised Beta function introduced by Chaudhry {\it et al.\/} [J. Comp. Appl. Math. {\bf 78} (1997) 19--32] defined by \[B(x,y;p)=\int_0^1 t^{x-1} (1-t)^{y-1} \ex…
On an extension of extended Beta and hypergeometric functions
R. K. Parmar, P. Chopra, R. B. Paris
Motivated mainly by certain interesting recent extensions of the Gamma, Beta and hypergeometric functions, we introduce here new extensions of the Beta function, hypergeometric and…