Polinomios de Bessel mediante gramáticas independientes del contexto
Bessel polynomials by context-free grammars
DOI:
https://doi.org/10.24054/bistua.v22i2.2932Palabras clave:
Polinomios de Bessel, Operador derivada formal, Gramáticas independientes del contextoResumen
Los polinomios de Bessel son una familia de polinomios ortogonales yn(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 yn(x)=(2n-1)xyn-1(x)+yn-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 yn(x)=(nx+1)yn-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.
Descargas
Citas
Chen, W.Y., Context-free grammars, differential operators and formal power series. Theoretical Computer Science 117 (1993) 113-129. https://doi.org/10.1016/0304-3975(93)90307-F
Chen W.Y., Fu A.M., Context-free grammars for permutations and increasing trees. Advances in Applied Mathematics 82 (2017) 58-82. https://doi.org/10.1016/j.aam.2016.07.003
Chen W.Y., Yang H.R., A context-free grammar for the Ramanujan-Shor polynomials. Advances in Applied Mathematics 126 (2021) 101908. https://doi.org/10.1016/j.aam.2019.04.005
Doha E.H., Ahmed H.M., On the coefficients of integrated expansions of Bessel polynomials. Journal of Computational and Applied Mathematics 187(1) (2006), 58-71. https://doi.org/10.1016/j.cam.2005.03.036
Gould H., Quaintance J., Double fun with double factorials. Mathematics Magazine 85(3) (2012) 177-192. https://doi.org/10.4169/math.mag.85.3.177
Hao R.X., Wang L.X., Yang H.R., Context-free grammars for triangular arrays. Acta Mathematica Sinica 31 (2015) 445-455. https://doi.org/10.1007/s10114-015-4209-5
Krall H.L., Frink O., A new class of orthogonal polynomials: The Bessel polynomials. Transactions of the American Mathematical Society 65(1) (1949) 100-115.
Ma S.M., Some combinatorial arrays generated by context-free grammars. European journal of combinatorics 34(7) (2013) 1081-1091. https://doi.org/10.1016/j.ejc.2013.03.002
Ma S.M., Ma J., Yeh Y.N. Zhu B.X., Context-free grammars for several polynomials associated with Eulerian polynomials. The Electronic Journal of Combinatorics 25(1) (2018) P1.31. https://doi.org/10.37236/6979
Ma S.M., Yeh Y.N., Eulerian polynomials, Stirling permutations of the second kind and perfect matchings. The Electronic Journal of Combinatorics 24(4) (2017) P4.27. https://doi.org/10.37236/7288
Ma S.M., Mansour T., Schork M., Normal ordering problem and the extensions of the Stirling grammar. Russian Journal of Mathematical Physics 21 (2014) 242-255. https://doi.org/10.1134/S1061920814020095
Rather N.A., Wani M.S., Dar I., On the Enestr"om-Kakeya theorem. Applied Mathematics E-Notes 22 (2022), 660-667.
Triana J., De Castro R., Grammars and multifactorial numbers. Global Journal of Pure and Applied Mathematics 15(3) (2019) 251-259.
Triana J., De Castro R., The formal derivative operator and multifactorial numbers. Revista Colombiana de Matem'aticas 53(2) (2019) 125-137. https://doi.org/10.15446/recolma.v53n2.85522
Triana J., $r$-Stirling numbers of the second kind through context-free grammars. Journal of automata languages and combinatorics 27(4) (2022) 323-333. https://doi.org/10.25596/jalc-2022-323
Zhou R.R., Yeh, J., Ren F., Context-free grammars for several triangular arrays. Axioms 11(6) (2022) 1-10. https://doi.org/10.3390/axioms11060297
Zhu B.X., Yeh Y.N., Lu Q., Context-free grammars, generating functions and combinatorial arrays. European journal of combinatorics 78 (2019) 236-255. https://doi.org/10.1016/j.ejc.2019.02.007
Archivos adicionales
Publicado
Versiones
- 2024-10-24 (2)
- 2024-08-21 (1)
Cómo citar
Número
Sección
Licencia
Derechos de autor 2024 © Autores; Licencia Universidad de Pamplona
Esta obra está bajo una licencia internacional Creative Commons Atribución-NoComercial-SinDerivadas 4.0.
© Autores; Licencia Universidad de Pamplona.
