New results on the associated Meixner, Charlier, and Krawtchouk polynomials

References

• Chihara TS. An introduction to orthogonal polynomials. New York: Gordon and Breach; 1978.
   Google Scholar
• Koekoek R, Lesky PA, Swarttouw RF. Hypergeometric orthogonal polynomials and their q-analogues. Berlin: Springer-Verlag; 2010. (Springer Monogr Math).
   Google Scholar
• Ismail MEH, Letessier J, Valent G, et al. Two families of associated Wilson polynomials. Canad J Math. 1990;42:659–695. doi: 10.4153/CJM-1990-035-4
   Web of Science ®Google Scholar
• Ismail MEH, Letessier J, Valent G, et al. Some results on associated Wilson polynomials. In: Brezinski C, et al., editors. Orthogonal polynomials and their applications. Basel, Switzerland: J. C. Baltzer A.G.; 1991. p. 293–298. (IMACS Ann. Comput. Appl. Math., vol: 9).
   Google Scholar
• Ismail MEH, Rahman M. The associated Askey-Wilson polynomials. Trans Amer Math Soc. 1991;328:201–237. doi: 10.1090/tran/1991-328-01
   Web of Science ®Google Scholar
• Wimp J. Explicit formulas for the associated Jacobi polynomials and some applications. Canad J Math. 1987;39:983–1000. doi: 10.4153/CJM-1987-050-4
   Web of Science ®Google Scholar
• Lewanowicz S. Results on the associated Jacobi and Gegenbauer polynomials. J Comput Appl Math. 1993;49:137–143. doi: 10.1016/0377-0427(93)90144-Z
   Web of Science ®Google Scholar
• Askey R, Wimp J. Associated Laguerre and Hermite Polynomials. Proc Roy Soc Edinburgh A. 1984;96:15–37. doi: 10.1017/S0308210500020412
   Google Scholar
• Luo MJ, Raina RK. Generating functions of Pollaczek polynomials: a revisit. Integral Transf Spec Funct. 2019;30:893–919. doi: 10.1080/10652469.2019.1636373
   Web of Science ®Google Scholar
• Rahman M. The associated classical orthogonal polynomials. In: Special functions 2000: current perspective and future directions. Dordrecht: Kluwer Acad Publisher; 2001. p. 255–279. ((Tempe, AZ), Volume 30 of NATO Sci. Ser. II, Math. Phys. Chem).
   Google Scholar
• Ismail MEH, Letessier J, Valent G. Linear birth and death models and associated Laguerre and Meixner polynomials. J Approx Theory. 1988;55:337–348. doi: 10.1016/0021-9045(88)90100-1
   Web of Science ®Google Scholar
• Ahbli K, Mouayn Z. A generating function and formulae defining the first-associated Meixner-Pollaczek polynomials. Integral Transf Spec Funct. 2018;29(5):352–366. doi: 10.1080/10652469.2018.1435647
   Web of Science ®Google Scholar
• Ali ST, Mouayn Z, Ahbli K. Nonlinear coherent states associated with a measure on the positive real half line. Complex Anal Oper Theory. 2020;24(1):28 pp.
   Google Scholar
• Hendriksen E. Associated Jacobi-Laurent polynomials. J Comput Appl Math. 1990;32:125–141. doi: 10.1016/0377-0427(90)90424-X
   Web of Science ®Google Scholar
• Barrucand P, Dickinson D. On the associated Legendre polynomials. In: Orthogonal expansions and their continuous analogues. Carbondale: Southern Illinois University; 1967.
   Google Scholar
• Bustoz J, Ismail MEH. The associated ultraspherical orthogonal polynomials and their q-analogues. Canad J Math. 1982;34:718–736. doi: 10.4153/CJM-1982-049-6
   Web of Science ®Google Scholar
• Ismail MEH, Letessier J, Valent G, et al. Associated Wilson polynomials. Canad J Math. 1990;42:659–695. doi: 10.4153/CJM-1990-035-4
   Web of Science ®Google Scholar
• Rahman M. Some generating functions for the associated Askey-Wilson polynomials. J Comput Appl Math. 1996;68(1–2):287–296. doi: 10.1016/0377-0427(95)00249-9
   Web of Science ®Google Scholar
• Gupta DP, Ismail MEH, Masson DR. Associated continuous Hahn polynomials. Canad J Math. 1991;43:1263–1280. doi: 10.4153/CJM-1991-072-3
   Web of Science ®Google Scholar
• Lewanowicz S. Results on the associated classical orthogonal polynomials. J Comput Appl Math. 1995;65:215–231. doi: 10.1016/0377-0427(95)00112-3
   Web of Science ®Google Scholar
• Drake D. The combinatorics of associated Hermite polynomials. Eur J Combin. 2009;30:1005–1021. doi: 10.1016/j.ejc.2008.05.009
   Web of Science ®Google Scholar
• Wimp J. Pollaczek polynomials and Padé approximants: some closed-form expressions. J Comput Appl Math. 1990;32:301–310. doi: 10.1016/0377-0427(90)90440-B
   Web of Science ®Google Scholar
• Ismail MEH. Classical and quantum orthogonal polynomials in one variable. Cambridge: Cambridge University Press; 2005. (Encyclopedia of mathematics and its applications; 96).
   Google Scholar
• Van Assche W. Orthogonal polynomials, associated polynomials and functions of the second kind. J Comput Appl Math. 1991;37(1–3):237–249. doi: 10.1016/0377-0427(91)90121-Y
   Web of Science ®Google Scholar
• Letessier J, Ronveaux A, Valent G. Fourth-order difference equation for the associated Meixner and Charlier polynomials. J Comput Appl Math. 1996;71:331–341. doi: 10.1016/0377-0427(96)87163-9
   Web of Science ®Google Scholar
• Foupouagnigni M, Hounkonnou MN, Ronveaux A. The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Δ-Laguerre-Hahn class. J Symb Comput. 1999;28(6):801–818. doi: 10.1006/jsco.1998.0340
   Web of Science ®Google Scholar
• Foupouagnigni M. Laguerre-Hahn orthogonal polynomials with respect to the Hahn operator: fourth-order difference equation for the rth associated and the Laguerre-Freud equations for the recurrence coefficients [dissertation]. Bénin: Université Nationale du Bénin; 1998.
   Google Scholar
• Nikiforov AF, Suslov SK, Uvarov VB. Classical orthogonal polynomials of a discrete variable. Berlin: Springer; 1991.
   Google Scholar
• Sghaier M, Zaatra M. The Dω-Laguerre-Hahn forms of class zero. Mediterr J Math. 2020;17(185):28 pp.
   Google Scholar
• Pollaczek F. On a family of orthogonal polynomials with four parameters. C R Acad Sci Paris. 1950;230:2254–2256. French.
   Google Scholar
• Andrews GE, Askey R, Roy R. Special functions. Cambridge: Cambridge University Press; 1999. (Encyclopedia of Mathematics and Its Applications; 71).
   Google Scholar
• Bailey WN. Generalized hypergeometric series. New York: Stechert-Hafner Service Agency; 1964. (Cambridge tracts in mathematics and mathematical physics; 32).
   Google Scholar
• Srivastava HM, Manocha HL. A treatise on generating functions. London: Ellis Horwood Limited; 1984.
   Google Scholar