In mathematics, the Tricomi–Carlitz polynomials or (Carlitz–)Karlin–McGregor polynomials are polynomials studied by Tricomi (1951) and Carlitz (1958) and Karlin and McGregor (1959), related to random walks on the positive integers.
They are given in terms of Laguerre polynomials by
They are special cases of the Chihara–Ismail polynomials.
References
edit- Carlitz, Leonard (1958), "On some polynomials of Tricomi", Boll. Un. Mat. Ital. (3), 13: 58–64, MR 0103303
- Karlin, Samuel; McGregor, James (1959), "Random walks", Illinois Journal of Mathematics, 3: 66–81, doi:10.1215/ijm/1255454999, ISSN 0019-2082, MR 0100927
- Tricomi, Francesco G. (1951), "A class of non-orthogonal polynomials related to those of Laguerre", Journal d'Analyse Mathématique, 1: 209–231, doi:10.1007/BF02790089, ISSN 0021-7670, MR 0051351
🔥 Top keywords: Akademia e Shkencave e RPS te ShqiperiseAlexandria Ocasio-CortezBilderberg GroupCristiano RonaldoDong XiaowanMinecraftOperation GladioPrimal cutRiot FestStrictly Come Dancing (series 7)Main PageSpecial:SearchKalki 2898 ADWikipedia:Featured picturesMartin MullICC Men's T20 World CupUEFA Euro 2024.xxxChris MartinA Quiet Place: Day One2024 ICC Men's T20 World CupProject 2025Joe BidenDua LipaCleopatraJamal Musiala2024 NHL entry draftVirat KohliColdplayDeaths in 2024Simone BilesUEFA European ChampionshipCeline DionCricket World CupThe Bear (TV series)Dakota JohnsonZac EfronCyndi LauperKasper Schmeichel2024 Copa AméricaRuben VargasBronny JamesBad Boys: Ride or DieElizabeth IAbu Ghraib torture and prisoner abuseNicole KidmanDonald TrumpRohit SharmaJasprit Bumrah