Info: The AGDM seminar is a joint seminar of the University of Vienna and TU Wien. In winter semesters, we meet on Tuesdays from 15:00 to 16:30 at the University of Vienna. In summer semesters, we meet on Tuesdays from 15:15 to 16:45 at TU Wien.
Since 2025, we use a mailing-list to advertise the seminar. You can register here.
Place: University of Vienna, Oskar-Morgenstern-Platz 1, BZ 09 (first room on the right on the 9th floor)
Time:Tuesday, 15:00-16:30
| Date: | Tuesday 13.01.2026 |
| Title: | Signed Generalized Stirling Polynomials and Generalized Hyperbolic Integrals |
| Speaker: | Abdulhafeez Abdulsalam (University of Vienna) |
| Abstract: | We revisit an integral originally evaluated by Malmsten in 1842 and present an alternative proof that leads naturally to generalizations of logarithmic–hyperbolic integrals. In this framework, we introduce the signed generalized Stirling polynomials of the first kind as a variant of the classical generalized Stirling polynomials. Explicit expressions for these polynomials are derived in terms of Stirling cycle numbers and complete Bell polynomials. These polynomials arise naturally in a generalization of Malmsten’s integral to all natural powers of the hyperbolic secant function. We further construct new families of integrals that share the structural features of Malmsten’s integral and show that they can be expressed naturally in terms of the signed generalized Stirling polynomials of the first kind. |
Maintaining a respectful environment is essential to fostering meaningful dialogue and intellectual growth. Participants are expected to refrain from any form of disrespectful or inappropriate behaviour, including offensive comments, harassment, or disruptive conduct. Questions and contributions should be constructive, relevant to the topic, and posed in a professional manner that encourages healthy academic exchange. Harassment of any kind—including verbal, moral or physical—will not be tolerated, and all attendees are urged to uphold these principles to ensure a safe and welcoming atmosphere for everyone.
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