Close-to-convexity of normalized Dini functions (Q2830662)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Close-to-convexity of normalized Dini functions |
scientific article; zbMATH DE number 6645461
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Close-to-convexity of normalized Dini functions |
scientific article; zbMATH DE number 6645461 |
Statements
Close-to-convexity of normalized Dini functions (English)
0 references
28 October 2016
0 references
Bessel functions of the first kind
0 references
close to convex functions
0 references
starlike functions
0 references
transcendental entire functions
0 references
zeros of Bessel functions
0 references
infinite product
0 references
The authors give necessary and sufficient conditions in order to ensure that some special combinations of Bessel functions of the first kind are starlike and their derivatives are close to convex (and hence starlike) in the open unit disc. For the proof they use a result of Shah and Trimble concerning transcendental entire functions and Mittag-Leffler expansion for Bessel functions of the first kind. Similar results have been proved for Bessel functions of the first kind in a series of papers written mostly by the first author and some of his collaborators.
0 references
