In mathematics, '''Denisyuk polynomials''' De<sub>''n''</sub>(''x'') or ''M''<sub>''n''</sub>(''x'') are generalizations of the Laguerre polynomials introduced by {{harvtxt|Denisyuk|1954}} given by the generating function{{sfnp|Boas|Buck|1958|p=41}}
<math display="block">\displaystyle \sum_{n=0}^\infty t^nM_n(x)=\frac 1{1+t}\exp\left(-\frac{xt}{1-t}\right).</math>
== Notes == {{reflist}}
==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
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