On the sequences of polynomials and their generating functions

  • Abdelkader Messahel University of Sciences and Technology Houari Boumedienne (USTHB)
  • Miloud Mihoubi University of Sciences and Technology Houari Boumedienne (USTHB)

Resumen

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.

Descargas

La descarga de datos todavía no está disponible.

Biografía del autor/a

Abdelkader Messahel, University of Sciences and Technology Houari Boumedienne (USTHB)

USTHB, Faculty of Mathematics, RECITS Laboratory, PHD.

Miloud Mihoubi, University of Sciences and Technology Houari Boumedienne (USTHB)

USTHB, Faculty of Mathematics, RECITS Laboratory, Professor.

Citas

P. Appell, Sur une classe de polynomes, Ann. Sci. Ecole Norm. Sup. 9 (1880), 119-144. https://doi.org/10.24033/asens.186

A. Z. Broder, The r-Stirling numbers, Discrete Math., 49, 241-259, (1984). https://doi.org/10.1016/0012-365X(84)90161-4

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

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

M. S. Maamra and M. Mihoubi, The (r1, . . . , rp)-Bell polynomials, Integers, 14, #A34, (2014).

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

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

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

M. Mihoubi, Bell polynomials and binomial type sequences. Discrete Math. 308, 2450-2459, (2008). https://doi.org/10.1016/j.disc.2007.05.010

M. Mihoubi and M. Sahari, On some polynomials applied to the theory of hyperbolic differential equations, Submitted.

M. Mihoubi and M. Sahari, On a class of polynomials connected to Bell polynomials, Arxiv (2018), avalaible at http://arxiv.org/abs/1801.01588v2

J. Riordan, Combinatorial Identities, John Wiley, New York, (1968).

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

K. R. Stromberg, Introduction to classical real analysis, Wadsworth, (1981).

H. S. Wilf, generatingfunctionology, 2nd edition. Academic Press, San Diego, (1994).

Publicado
2022-01-26
Sección
Research Articles