Some Inequalities for Modified Bessel Functions

By Andrea Laforgia, Pierpaolo Natalini. 2010

103 citations recorded by the source corpus.

We denote by and the Bessel functions of the first and third kinds, respectively. Motivated by the relevance of the function , , in many contexts of applied mathematics and, in particular, in some elasticity problems Simpson and Spector (1984), we establish new inequalities for . The results are based on the recurrence relations for and and the Turán-type inequalities for such functions. Similar investigations are developed to establish new inequalities for .

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/706417532310379601d7fdb28b3b7b299940fec1

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Turán type inequalities for modified Bessel functions (2010, background): “See [6, 26] for more details and also [2, 3, 4, 7, 8, 24, 25, 27, 34] for more details on Turán type inequalities.”
Bounds for ratios of modified Bessel functions and associated Turán-type inequalities (2011, methodology): “[18] A.”
Bounds for modified Bessel functions of the first and second kinds (2010, background): “After this paper was already in the press we found the papers [42, 52, 53], which are closely related to this paper.”
A new type of sharp bounds for ratios of modified Bessel functions (2016, background): “See [12] and references cited therein for additional examples of application of these bounds; see also [4, 1, 9, 8, 6, 2] for additional papers exploring different methods for bounding these ratios.”