Some Remarks on the Location of Non-Asymptotic Zeros of Whittaker and Kummer Hypergeometric Functions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Bulletin des Sciences Mathématiques Année : 2021

Some Remarks on the Location of Non-Asymptotic Zeros of Whittaker and Kummer Hypergeometric Functions

Résumé

This paper focuses on the location of the non-asymptotic zeros of Whittaker and Kummer confluent hypergeometric functions. Based on a technique by E. Hille for the analysis of solutions of some second-order ordinary differential equations, we characterize the sign of the real part of zeros of Whittaker and Kummer functions and provide estimates on the regions of the complex plane where those zeros can be located. Our main result is a correction of a previous statement by G. E. Tsvetkov whose propagation has induced mistakes in the literature. In particular, we review some results of E. B. Saff and R. S. Varga on the error of Padé's rational approximation of the exponential function, which are based on the latter.
Fichier principal
Vignette du fichier
Whittaker.pdf (166.57 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03250426 , version 1 (04-06-2021)
hal-03250426 , version 2 (17-06-2021)

Identifiants

Citer

Islam Boussaada, Guilherme Mazanti, Silviu-Iulian Niculescu. Some Remarks on the Location of Non-Asymptotic Zeros of Whittaker and Kummer Hypergeometric Functions. Bulletin des Sciences Mathématiques, 2021, 174, Paper No. 103093, 12 pp. ⟨10.1016/j.bulsci.2021.103093⟩. ⟨hal-03250426v2⟩
188 Consultations
193 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More