3 papers
math.NT2026
Wallis-type products with polynomial exponents and the Dirichlet beta function at negative integers
Joshua W. E. Farrell
We develop a methodology for designing infinite products of rational blocks whose exponents are polynomials in the index . Matching power sums of the slot constants through orde…
cs.CY2025
Securing External Deeper-than-black-box GPAI Evaluations
Alejandro Tlaie, Jimmy Farrell
This paper examines the critical challenges and potential solutions for conducting secure and effective external evaluations of general-purpose AI (GPAI) models. With the exponenti…
math.NT2019
Generalising the Wallis Product
Joshua W. E. Farrell
In 1655, John Wallis whilst at the University of Oxford discovered the famous and beautiful formula for pi, now known as Wallis' Product. Since then, several analogous formulae hav…