Tur\'an type inequalities for general Bessel functions

TL;DR

This paper establishes Turán type inequalities, monotonicity, bounds, and series representations for general Bessel functions, enhancing understanding of their properties through recurrence relations and asymptotic analysis.

Contribution

It introduces new Turán type inequalities and detailed properties for general Bessel functions, expanding theoretical knowledge in special functions.

Findings

Derived Turán type inequalities for general Bessel functions

Established bounds and monotonicity of the logarithmic derivative

Identified series representations and extrema of the Turánian

Abstract

In this paper some Tur\'an type inequalities for the general Bessel function, monotonicity and bounds for its logarithmic derivative are derived. Moreover we find the series representation and the relative extrema of the Tur\'anian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.