Turán-Type Inequalities for Some Lommel Functions of the First Kind

In this paper certain Turán-type inequalities for some Lommel functions of the first kind are deduced. The key tools in our proofs are the infinite product representation for these Lommel functions of the first kind, a classical result of Pólya on the zeros of some particular entire functions, and t...

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Bibliographic Details
Published in:Proceedings of the Edinburgh Mathematical Society 2016-08, Vol.59 (3), p.569-579
Main Authors: Baricz, Árpád, Koumandos, Stamatis
Format: Article
Language:English
Subjects:
Entire functions
Functions (mathematics)
Inequalities
Joints
Mathematical analysis
Mathematical functions
Proving
Representations
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Summary:In this paper certain Turán-type inequalities for some Lommel functions of the first kind are deduced. The key tools in our proofs are the infinite product representation for these Lommel functions of the first kind, a classical result of Pólya on the zeros of some particular entire functions, and the connection of these Lommel functions with the so-called Laguerre–Pólya class of entire functions. Moreover, it is shown that in some cases Steinig's results on the sign of Lommel functions of the first kind combined with the so-called monotone form of l’Hospital's rule can be used in the proof of the corresponding Turán-type inequalities.
ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091515000413