Bessel polynomials by context-free grammars
Polinomios de Bessel mediante gramáticas independientes del contexto
DOI:
https://doi.org/10.24054/bistua.v22i2.2932Keywords:
Bessel polynomials, formal derivative operator, context-free grammarsAbstract
The Bessel polynomials are an orthogonal family of polynomials yn(x) introduced as solutions of the second-order differential equation x2y''+2(x+1)y'=n(n+1)y, they satisfy the recurrence relation yn(x)=(2n-1)xyn-1(x)+yn-2(x), where y1(x)=x+1 y y0(x)=1. In terms of derivatives, Bessel polynomials can be described by the recurrence yn(x)=(nx+1)yn-1(x) + x2y'n-1(x). In this paper, we study the connection between Bessel polynomials and context-free grammars through the formal derivative operator, and we prove some identities of this family of polynomials.
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