The talk today will be delivered by Abdulhafeez Abdulsalam, one of the 2022 Spirit of Ramanujan Fellows.
Talk Announcement:
Title: Signed Generalized Stirling Polynomials, Nested Sums, and Hyperbolic Secant Integral Identities
Speaker: Abdulhafeez Abdulsalam
When: September 17, 2026, 5:00 PM- 6:00 PM IST (1:30 PM CEST)
Where: Zoom:
Live Link: https://youtube.com/
Abstract: We study signed generalized Stirling polynomials $P_k(m,x)$ arising in closed forms for Malmsten-type hyperbolic secant integrals. Their product structure is used to prove recurrences, gamma--polygamma formulas for $P_{m-s}(m,x)$, a central vanishing identity, a finite approximation to $\cosh \pi x$, and a limit formula for $\pi$. We identify these polynomials as signed residues of the equal-period Barnes multiple zeta function, derive their reflection formula, and obtain finite parity-cancellation and Stirling cycle-number identities, including a comparison with a classical Meixner--Pollaczek orthogonal family. We also evaluate finite nested sums built from the sequence $\chi_n$. Fixing the lower bounds turns these sums into coefficient-counting problems: common lower bounds give binomial coefficients and staircase bounds give Catalan numbers. Combining these counts with known formulas for $\chi_j$ yields explicit hyperbolic-secant integral evaluations involving Catalan's constant, zeta values,and polygamma values. A Wolfram Language package accompanies the formulas. This work is joint with Michael Schlosser.
No comments:
Post a Comment