Turán determinants of Bessel functions

Details Turán determinants of Bessel functions Turán determinants of Bessel functions

2011-01-24

arxiv.org/abs/1101.4624v2

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

In this paper first we survey the Tur\'an type inequalities and related problems for the Bessel functions of the first kind. Then we extend the known higher order Tur\'an 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 Tur\'an determinants of Bessel functions of the first kind. At the end of the paper we prove a Tur\'an type inequality for the Bessel functions of the second kind.

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