Bessel polynomials by context-free grammars: Polinomios de Bessel mediante gramáticas independientes del contexto

Juan Triana

doi:10.24054/bistua.v22i2.2932

Autores/as

Juan Triana Universitaria Agustiniana

DOI:

https://doi.org/10.24054/bistua.v22i2.2932

Palabras clave:

Polinomios de Bessel, Operador derivada formal, Gramáticas independientes del contexto

Resumen

Los polinomios de Bessel son una familia de polinomios ortogonales y_n(x) presentados como solución de la ecuación diferencial de segundo orden x²y''+2(x+1)y'=n(n+1)y; estos polinomios satisfacen la recurrencia y_n(x)=(2n-1)xy_n-1(x)+y_n-2(x), con y₁(x)=x+1 y y₀(x)=1. En términos de la derivada, los polinomios de Bessel pueden obtenerse mediante la recurrencia y_n(x)=(nx+1)y_n-1(x) + x²y'_n-1(x). En este artículo estudiamos la conexión entre los polinomios de Bessel y las gramáticas independientes del contexto mediante el operador derivada formal, además probamos algunas identidades de los polinomios de Bessel.

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Citas

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Polinomios de Bessel mediante gramáticas independientes del contexto