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- Title
Characterization of the Bernoulli polynomials via the Raabe functional equation.
- Authors
Farhi, Bakir
- Abstract
The purpose of the present paper is to show that in certain classes of real (or complex) functions, Bernoulli polynomials are essentially the only ones satisfying the Raabe functional equation. For the class of real 1-periodic functions which are expandable as Fourier series, we point out new solutions of the Raabe functional equation, not related to Bernoulli polynomials. Furthermore, we will give for the considered classes various proofs, making the mathematical content of the paper quite rich.
- Subjects
BERNOULLI polynomials; FOURIER series; FUNCTIONAL equations; PERIODIC functions
- Publication
Aequationes Mathematicae, 2024, Vol 98, Issue 3, p787
- ISSN
0001-9054
- Publication type
Article
- DOI
10.1007/s00010-023-00984-9