On the sequences of polynomials and their generating functions
DOI:
https://doi.org/10.5269/bspm.44526Resumen
In this article, we will give first of all, an identity having interesting applications on polynomials and some combinatorial sequences. Secondly, we will refer two interesting formulas on generating functions of polynomials. Our results are illustrated in fact, by some comprehensive examples.
Referencias
1. P. Appell, Sur une classe de polynomes, Ann. Sci. Ecole Norm. Sup. 9 (1880), 119-144. https://doi.org/10.24033/asens.186
2. A. Z. Broder, The r-Stirling numbers, Discrete Math., 49, 241-259, (1984). https://doi.org/10.1016/0012-365X(84)90161-4
3. J. W. Brown, New generating functions for classical polynomials, Proc. Amer. Math. Soc., 21, 263-268, (1969). https://doi.org/10.1090/S0002-9939-1969-0236438-8
4. J. D. E. Konhauser, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 21, 303-314, (1967). https://doi.org/10.2140/pjm.1967.21.303
5. M. S. Maamra and M. Mihoubi, The (r1, . . . , rp)-Bell polynomials, Integers, 14, #A34, (2014).
6. Z. A. Melzak, V. D. Gokhale, and W. V. Parker, Advanced problems and solutions: 4458, Amer. Math. Monthly, 60 (1), 53-54, (1953). https://doi.org/10.2307/2306491
7. Z. A. Melzak, D. J. Newman, P. Erdos, G. Grossman, and M. R. Spiegel, Advanced problems and solutions: 4458, Amer. Math. Monthly, 58 (9), p. 636, (1951). https://doi.org/10.2307/2306368
8. I. Mezo, On the maximum of r-Stirling numbers, Adv. Appl. Math., 41, 293-306, (2008). https://doi.org/10.1016/j.aam.2007.11.002
9. M. Mihoubi, Bell polynomials and binomial type sequences. Discrete Math. 308, 2450-2459, (2008). https://doi.org/10.1016/j.disc.2007.05.010
10. M. Mihoubi and M. Sahari, On some polynomials applied to the theory of hyperbolic differential equations, Submitted.
11. M. Mihoubi and M. Sahari, On a class of polynomials connected to Bell polynomials, Arxiv (2018), avalaible at http://arxiv.org/abs/1801.01588v2
12. J. Riordan, Combinatorial Identities, John Wiley, New York, (1968).
13. H. M. Sristava and J.P. Singhal, New generating functions for Jacobi and related polynomials, J. Math. Anal. Appl., 41 (1973), pp. 748-752. https://doi.org/10.1016/0022-247X(73)90244-8
14. K. R. Stromberg, Introduction to classical real analysis, Wadsworth, (1981).
15. H. S. Wilf, generatingfunctionology, 2nd edition. Academic Press, San Diego, (1994).
2. A. Z. Broder, The r-Stirling numbers, Discrete Math., 49, 241-259, (1984). https://doi.org/10.1016/0012-365X(84)90161-4
3. J. W. Brown, New generating functions for classical polynomials, Proc. Amer. Math. Soc., 21, 263-268, (1969). https://doi.org/10.1090/S0002-9939-1969-0236438-8
4. J. D. E. Konhauser, Biorthogonal polynomials suggested by the Laguerre polynomials, Pacific J. Math. 21, 303-314, (1967). https://doi.org/10.2140/pjm.1967.21.303
5. M. S. Maamra and M. Mihoubi, The (r1, . . . , rp)-Bell polynomials, Integers, 14, #A34, (2014).
6. Z. A. Melzak, V. D. Gokhale, and W. V. Parker, Advanced problems and solutions: 4458, Amer. Math. Monthly, 60 (1), 53-54, (1953). https://doi.org/10.2307/2306491
7. Z. A. Melzak, D. J. Newman, P. Erdos, G. Grossman, and M. R. Spiegel, Advanced problems and solutions: 4458, Amer. Math. Monthly, 58 (9), p. 636, (1951). https://doi.org/10.2307/2306368
8. I. Mezo, On the maximum of r-Stirling numbers, Adv. Appl. Math., 41, 293-306, (2008). https://doi.org/10.1016/j.aam.2007.11.002
9. M. Mihoubi, Bell polynomials and binomial type sequences. Discrete Math. 308, 2450-2459, (2008). https://doi.org/10.1016/j.disc.2007.05.010
10. M. Mihoubi and M. Sahari, On some polynomials applied to the theory of hyperbolic differential equations, Submitted.
11. M. Mihoubi and M. Sahari, On a class of polynomials connected to Bell polynomials, Arxiv (2018), avalaible at http://arxiv.org/abs/1801.01588v2
12. J. Riordan, Combinatorial Identities, John Wiley, New York, (1968).
13. H. M. Sristava and J.P. Singhal, New generating functions for Jacobi and related polynomials, J. Math. Anal. Appl., 41 (1973), pp. 748-752. https://doi.org/10.1016/0022-247X(73)90244-8
14. K. R. Stromberg, Introduction to classical real analysis, Wadsworth, (1981).
15. H. S. Wilf, generatingfunctionology, 2nd edition. Academic Press, San Diego, (1994).
Descargas
Publicado
2022-01-26
Número
Sección
Research Articles
Licencia
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
