A Generalization of Bohr-Mollerup's Theorem for Higher Order Convex Functions
- Author
- Jean-Luc Marichal
- Publication Year
- 2022
- Publisher
- Springer Cham
- Language
- English
- Document Type
- Book
- Faculty / Subject Heading
- Engineering
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This book 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.
Keywords: Mathematics and Statistics / Special Functions / Difference and Functional Equations / Difference Equation / Higher Order Convexity / Bohr-Mollerups Theorem / Principal Indefinite Sums / Gamma Function / Polygamma Functions / Hurwitz Zeta Function / Generalized Stieltjes Constants
