Denisyuk polynomials

In mathematics, Denisyuk polynomials De_n(x) or M_n(x) are generalizations of the Laguerre polynomials introduced by {{harvtxt|Denisyuk|1954}} given by the generating function{{sfnp|Boas|Buck|1958|p=41}}

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

Notes

References

{{citation

|last1 = Boas |first1 = Ralph P.

|last2 = Buck |first2 = R. Creighton

|title = Polynomial expansions of analytic functions

|url = https://books.google.com/books?id=eihMuwkh4DsC

|publisher = Springer-Verlag

|location = Berlin, New York

|series = Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge.

|mr = 0094466

|year = 1958

|volume = 19

|isbn = 978-3-662-23179-1

}}

{{citation

|last1 = Denisyuk |first1 = I. M.

|title = Some integrals, matrices and approximations connected with polynomials analogous to the Laguerre polynomials

|language = Ukrainian

|mr = 0067241

|year = 1954

|journal = Akademiya Nauk Ukrainskoui SSR. Doklady. Seriya A. Fiziko-Matematicheskie I Tekhnicheskie Nauki

|issn = 0201-8446

|volume = 1954

|pages = 239–242

}}

Category:Polynomials