9 citations · 76 across the 82 of their papers we have counts for
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On some Féjer-type trigonometric sums
R. B. Paris
We examine the four Féjer-type trigonometric sums of the form \[S_n(x)=\sum_{k=1}^n \frac{f(g(kx))}{k}\qquad (0<x<π)\] where , are chosen to be either or $\co…
Asymptotics of some generalised sine-integrals
R B Paris
We obtain the asymptotic expansion for large integer of a generalised sine-integral \[\int_0^\infty\left(\frac{\sin\,x}{x}\right)^{n}dx\] by utilising the saddle-point method.…
A note on an extension of Gelfond's constant
A. K. Rathie, R. B. Paris
The aim of this note is to provide a natural extension of Gelfond's constant using a hypergeometric function approach. An extension is also found for the square root of this…
A note on a generalization of two well-known Cominatorial identities via a Hypergeometric series approach
Arjun K. Rathie, Insuk Kim, Richard B. Paris
In this note, we aim to provide generalizations of (i) Knuth's old sum (or Reed Dawson identity) and (ii) Riordan's identity using a hypergeometric series approach.
On a new result for the hypergeometric function
A. K. Rathie, R. B. Paris
The aim of this note is to provide a new identity connected with the Gauss hypergeometric function. This is achieved using results of certain combinatorial identities and a hyperge…
Extensions of beta and related functions
M. Ghayasuddin, M. Ali, R. B. Paris
In this paper, we introduce and investigate a new extension of the beta function by means of an integral operator involving a product of Bessel-Struve kernel functions. We also def…