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.
Signed Generalized Stirling Polynomials and Generalized Hyperbolic Integrals
13.01.2026 15:00 - 16:00
Organiser:
Ilse Fischer and Michael Schlosser
Location: