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Turán determinants of Bessel functions
-
Árpád Baricz
and
Tibor K. Pogány
Published/Copyright:
November 5, 2011
Abstract.
In this paper first we survey the Turán type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Turán type inequalities for Bessel functions of the first kind to real parameters and we deduce new closed integral representation formulas for the second kind Neumann type series of Bessel functions of the first kind occurring in the study of Turán determinants of Bessel functions of the first kind. At the end of the paper we prove a Turán type inequality for the Bessel functions of the second kind.
Keywords: Bessel functions of the first kind; Bessel functions of
the second kind; Turán type inequalities; Laguerre type
inequalities; Turán and Hankel determinants; entire functions; Laguerre–Pólya class; Neumann series of Bessel functions of the
first kind; recurrence relations; integral representations; bounds
Received: 2011-02-07
Revised: 2011-09-27
Published Online: 2011-11-05
Published in Print: 2014-01-01
© 2014 by Walter de Gruyter Berlin Boston
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Keywords for this article
Bessel functions of the first kind;
Bessel functions of
the second kind;
Turán type inequalities;
Laguerre type
inequalities;
Turán and Hankel determinants;
entire functions;
Laguerre–Pólya class;
Neumann series of Bessel functions of the
first kind;
recurrence relations;
integral representations;
bounds
Articles in the same Issue
- Masthead
- Pseudovarieties generated by Brauer type monoids
- On some arithmetic properties of Siegel functions (II)
- Perfect vector alignment of the vorticity and the vortex stretching is one forever
- Frobenius groups of automorphisms and their fixed points
- Schubert calculus and the Hopf algebra structures of exceptional Lie groups
- The sovability of norm, bilinear and quadratic equations over finite fields via spectra of graphs
- Periodicity in the stable representation theory of crystallographic groups
- Sums of Fourier coefficients of a Maass form for SL3(ℤ) twisted by exponential functions
- The rational classification of links of codimension > 2
- On the classifying space for proper actions of groups with cyclic torsion
- Turán determinants of Bessel functions
