Turán-Type Inequalities for Some Lommel Functions of the First Kind
Ημερομηνία
2016Source
Proceedings of the Edinburgh Mathematical SocietyVolume
59Issue
3Pages
569-579Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
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. © 2016 Edinburgh Mathematical Society.