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- Publisher
- Springer Journals
- Copyright
- Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
- ISSN
- 1664-2368
- eISSN
- 1664-235X
- DOI
- 10.1007/s13324-021-00525-0
- Publisher site
- See Article on Publisher Site
Abstract
We are concerned with a special sequence of Appell polynomials, related to the Rényi and Tsallis entropies for the binomial distribution. The generating function is investigated: it is logarithmically convex and has remarkable connections with the modified Bessel function I0(t)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$I_0(t)$$\end{document} and with the index of coincidence for Poisson distribution. The specific form of the Appell polynomials leads to specific properties of the associated Jakimovski–Leviatan operators.
Journal
Analysis and Mathematical Physics – Springer Journals
Published: Mar 31, 2021