Denisyuk polynomials

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

$\displaystyle \sum_{n=0}^\infty t^nM_n(x)=\frac 1{1+t}\exp-\frac{xt}{1-t}$

(Boas & Buck 1958, p.41).

See also

References

• Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., 19, Berlin, New York: Springer-Verlag, MR0094466, http://books.google.com/books?id=eihMuwkh4DsC 
• Denisyuk, I. M. (1954), "Some integrals, matrices and approximations connected with polynomials analogous to the Laguerre polynomials" (in Ukrainian), Akademiya Nauk Ukrainskoui SSR. Doklady. Seriya A. Fiziko-Matematicheskie i Tekhnicheskie Nauki 1954: 239–242, ISSN 0201-8446, MR0067241