Jean-Luc Marichal and Naïm Zenaïdi recently published “A Generalization of Bohr-Mollerup’s Theorem for Higher Order Convex Functions”, a distinguished book on the developments in Mathematics.
Springer Developments in Mathematics is a prestigious book series specially designed for monographs that bring new important contributions in pure and applied mathematics.
This volume develops a far-reaching generalization of Bohr-Mollerup’s theorem to higher order convex functions, along lines initiated by Wolfgang Krull, Roger Webster, and some others but going considerably further than past work. In particular, this generalization shows using elementary techniques that a very rich spectrum of functions satisfy analogues of several classical properties of the gamma function, including Bohr-Mollerup’s theorem itself, Euler’s reflection formula, Gauss’ multiplication theorem, Stirling’s formula, and Weierstrass’ canonical factorization.
This volume is also an opportunity to honor the 100th anniversary of Bohr-Mollerup’s theorem and to spark the interest of a large number of researchers in this beautiful theory.
Download it here: https://link.springer.com/book/10.1007/978-3-030-95088-0