engleski

Turán determinants of Bessel functions

In this paper our aim is to survey the Turán type inequalities and related problems for the Bessel functions of the first kind. Moreover, 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 formulae 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.

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-P\lya class; Neumann series of Bessel functions of the first kind; Recurrence relations; Integral representations; Bounds.

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