Meixner polynomials and their properties

1Makarov, VL
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 7:3-8
Section: Mathematics
Language: Ukrainian

A number of properties of a special case of Meixner polynomials given by their generating function are investigated.
These polynomials arise when applying the Cayley transformation method to solving the first bounda ryvalue
problem for an abstract differential equation of the second order with an unbounded operator coefficient.

Keywords: Cayley transformation method, generating function, Green function, Meixner polynomials, recurrent equations

1. Meixner, J. (1934). Orthogonale Polynomsysteme mit einer besonderen Gestalt der erzeugenden Funktion. J. London Math. Soc., s1-9, Iss. 1, pp. 6-13.
2. Szeg’o, G. (1962). Orthogonal polynomials. Moscow: Fizmatlit (in Russian).
3. Gavrilyuk, I.P. & Makarov, V.L. (2004). Strongly positive operators and numerical algorithms without accuracy saturation. Proceedings of the Institute of Mathematics of the NAS of Ukraine. (Vol. 52). Kyiv (in Russian).
4. Gavrilyuk, I.P. & Makarov, V.L. (1999). Explicit and approximate solutions of second order differential equations in Hilbert and Banach spaces. Numer. Funct. Anal. Optim., 20, pp. 695-717.
5. Gavrilyuk, I.P. & Makarov, V.L. (1994). The Cayley transform and the solution of an initial problem for a first order differential equation with an unbounded operator coefficient in Hilbert space. Numer. Funct. Anal. Optim., 15, pp. 583-598.
6. Li, X. & Chen, C.-P. (2007). Inequalities for the gamma function. J. Ineq. Pure and Appl. Math., 8, Iss. 1, Art. 28, 3 pp.
7. Fikhtengol’ts, G.M. (1957). The fundamentals of mathematical analysis. (Vol. 2). Moscow: GITTL (in Russian).