In mathematics, Denisyuk polynomials De_n(x) or M_n(x) are generalizations of the Laguerre polynomials introduced by Denisyuk (1954) given by the generating function^[1]

$${\displaystyle \displaystyle \sum _{n=0}^{\infty }t^{n}M_{n}(x)={\frac {1}{1+t}}\exp -{\frac {xt}{1-t}}.}$$

Notes

References

• Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., vol. 19, Berlin, New York: Springer-Verlag, MR 0094466

• Denisyuk, I. M. (1954), "Some integrals, matrices and approximations connected with polynomials analogous to the Laguerre polynomials", Akademiya Nauk Ukrainskoui SSR. Doklady. Seriya A. Fiziko-Matematicheskie i Tekhnicheskie Nauki (in Ukrainian), 1954: 239–242, ISSN 0201-8446, MR 0067241