On the Inverse of the Linearization Coefficients of Bessel Polynomials

Abstract

In this contribution, we first present a new recursion relation fulfilled by the linearization coefficients of Bessel polynomials (LCBPs), which is different than the one presented by Berg and Vignat in 2008. We will explain why this new recursion formula is as important as Berg and Vignat’s. We introduce the matrix linearization coefficients of Bessel polynomials (MLCBPs), and we present some new results and some conjectures on these matrices. Second, we present the inverse of the connection coefficients with an application involving the modified Bessel function of the second kind. Finally, we introduce the inverse of the matrix of the linearization coefficients of the Bessel polynomials (IMLCBPs), and we present some open problems related to these IMLCBPs.

Keywords

• Bessel polynomials
• linearization coefficients
• integral formula of Boros and Moll
• student t-density
• differential equations