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15 papers · 1 filter
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…
Evolution of spheroidal dust in electrically active sub-stellar atmospheres
Craig R. Stark, Declan A. Diver
Understanding the source of sub-stellar polarimetric observations in the optical and near-infrared is key to characterizing sub-stellar objects and developing potential diagnostics…
Proposal of a Novel Bug Bounty Implementation Using Gamification
Jamie O'Hare, Lynsay A. Shepherd
Despite significant popularity, the bug bounty process has remained broadly unchanged since its inception, with limited implementation of gamification aspects. Existing literature…
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…
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…
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…