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...

A modification of standard Poincaré asymptotic expansions for functions defined by means of Laplace transforms is analyzed. This modification is based on an alternative power series expansion of the integrand, and the convergence properties are seen to be superior to those of the original asymptotic series. The resulting modified asymptotic expansion involves confluent hypergeometric functions ...

Abstract. The object of the present paper is to establish an integral formula involving Wright generalized Bessel function (or generalized Bessel-Maitland function) J ν,q (z) defined by Singh et al. [21], which is expressed in the terms of generalized (Wright) hypergeometric functions. Some interesting special cases involving Bessel functions, generalized Bessel functions, generalized Mittag-Le...

Integrated optical phased arrays for generating quasi-Bessel beams are proposed and experimentally demonstrated in a CMOS-compatible platform. Owing to their elongated central beams, Bessel beams have applications in a range of fields, including multiparticle trapping and laser lithography. In this Letter, continuous Bessel theory is manipulated to formulate the phase and amplitude conditions n...

Abstract. We work out the expression of the generalized Bessel function of B2-type derived in [4]. This is done using Dijskma and Koornwinder’s product formula for Jacobi polynomials and the obtained expression is given by multiple integrals involving only a normalized modified Bessel function and two symmetric Beta distributions. We think of that expression as the major step toward the explici...

Keywords: Generalized Marcum Q-function Non-central chi and chi-squared distribution Modified Bessel functions Log-concavity NBU property a b s t r a c t In this paper, we consider the generalized Marcum Q-function of order m > 0 real, defined by Q m ða; bÞ ¼ 1 a mÀ1 Z 1 b t m e À t 2 þa 2 2 I mÀ1 ðatÞdt; where a; b P 0, I m stands for the modified Bessel function of the first kind and the righ...

We consider both the bosonic and fermionic second quantization of spectral triples in presence a chemical potential. show that von Neumann entropy average energy Gibbs state defined by grand partition function can be expressed as actions. It turns out all action coefficients given terms modified Bessel functions. In case, we for entropy, limit when potential μ approaches 0, Riemann zeta functio...

Recently, harmonic imaging has been shown to increase image quality in medical imaging. This is believed to be caused by decreased sidelobes. It is also due to a decreased sensitivity to near-field aberrations owing to the lower transmission frequency, and the lower relative amplitude of the second harmonic in the near-field. One of the problems of limited diffraction beams has been the sidelob...