On the Log-Concavity of the Wright Function

• Type: Article in International Scientific Journal
• Date: 2023

Authors

Ferreira, RAC (Author) Other; Simon, T (Author) Other

Journal

Title: Constructive Approximation

ISSN: 0176-4276

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 0 Citations

Other information

Authenticus ID: P-00Z-6K5

DOI: 10.1007/s00365-023-09666-w

Abstract (EN): We investigate the log-concavity on the half-line of the Wright function phi(- alpha, beta,- x), in the probabilistic setting a is an element of (0, 1) and beta >= 0. Applications are given to the construction of generalized entropies associated to the corresponding Mittag-Leffler function. A natural conjecture for the equivalence between the log-concavity of the Wright function and the existence of such generalized entropies is formulated. The problem is solved for beta >= alpha and in the classical case beta = 1 - alpha of the MittagLeffler distribution, which exhibits a certain critical parameter alpha(*) = 0.771667... defined implicitly on the Gamma function and characterizing the log-concavity. We also prove that the probabilistic Wright functions are always unimodal, and that they are multiplicatively strongly unimodal if and only if beta >= alpha or alpha <= 1/2 and beta = 0.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 30