Integral representations and asymptotic expansions for the second type Neumann series of Bessel functions of the first kind

2023/12/03 by Romaniega, Álvaro
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2312.01438

Abstract

In this paper we study the following Bessel series ∑ _l=1^∞ J_l+m'(r)J_l+m(r)(l+β)^α for any m,m'∈ℤ, α∈ℝ and β>-1. They are a particular case of the second type Neumann series of Bessel functions of the first kind. More specifically, we derive fully explicit integral representations and study the asymptotic behavior with explicit terms. As a corollary, the asymptotic behavior of series of the derivatives of Bessel functions can be understood.

Related

• Integral representation for Bessel's functions of the first kind and\n Neumann series
• An expansion for the sum of a product of an exponential and a Bessel function
• The evaluation of infinite sums of products of Bessel functions
• Asymptotic expoansions of mathieu-Bessel series. I
• Two Neumann Series Expansions for the Sine and Cosine Integrals