In this paper some Turán 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 Turánian of general Bessel functions. The key tools in the proofs are the recurrence relations together with some asymptotic relations for Bessel functions.

h thii paper, an asymptotic expression of the incomplete gamma matrix function and integral expressions of Bessel matrix functions are given. Results are applied to study the asymptotic behavior of the modified Bessel function. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords-Bessel function, Incomplete gamma function, Asymptotics.

We demonstrate the generation of Bessel beams using an acousto-optic array based on a liquid filled cavity surrounded by a cylindrical multi-element ultrasound transducer array. Conversion of a Gaussian laser mode into a Bessel beam with tunable order and position is shown. Also higher-order Bessel beams up to the fourth order are successfully generated with experimental results very closely ma...

This paper is part of the collection initiated in [12], aiming to evaluate the entries in [8] and to provide some context. This table contains a large variety of entries involving the Bessel functions. The goal of the current work is to evaluate some entries in [8] where the integrand is an elementary function and the result involves the so-called modified Bessel function of the second kind, de...

A closed integral expression is derived for Neumann series of Bessel functions — a series of Bessel functions of increasing order — over the set of real numbers.

We report the creation of white-light, achromatic Bessel beams using a spatial light modulator and a prism to compensate for the dispersion. Unlike the Bessel beam created by a refractive axicon, this achromatic beam has a radial wavevector and hence an intensity cross-section which is independent of wavelength. The technique also lends itself to the generation of higher order Bessel beams with...

Recently Pogány and Süli [Proc. Amer. Math. Soc. 137(7) (2009), 2363–2368] derived a closed-form integral expression for Neumann series of Bessel functions of the first kind Jν . In this paper our aim is to establish analogous integral representations for the Neumann-type series of modified Bessel functions of the first kind Iν and for Bessel functions of the second kind Yν , Kν , and to give l...

We establish a simple relative trace formula for GSp(4) and inner forms with respect to Bessel subgroups to obtain a certain Bessel identity. From such an identity, one can hope to prove a formula relating central values of degree four spinor L-functions to squares of Bessel periods as conjectured by Böcherer. Under some local assumptions, we obtain nonvanishing results, i.e., a global Gross–Pr...

A theory of the recently discussed and demonstrated novel phenomenon of self-phase-matching [B.Glushko, B. Kryzhanovsky, and D. Sarkisyan, Phys. Rev. Lett. 71, 243 (1993)j is given by representing the conical beam, produced in the experiments, by a Bessel beam and as a superposition of Bessel beams. The predictions of the theory with the superposition of Bessel beams are in conformity with the ...