Narumi polynomials

In mathematics, the Narumi polynomials s_n(x) are polynomials introduced by Narumi (1929) given by the generating function

$\displaystyle \sum s_n(x)t^n/n! = \left(\frac{t}{\log(1+t)}\right)^a(1+t)^x$

(Roman 1984, 4.4), (Boas & Buck 1958, p.37)

See also

• Umbral calculus

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 
• Narumi, S. (1929), "On a power series having only a finite number of algebraico logarithmic singularities on its circle of convergence.", Tohoku Mathematical Journal 30: 185–201, JFM 55.0185.03, http://www.journalarchive.jst.go.jp/english/jnlabstract_en.php?cdjournal=tmj1911&cdvol=30&noissue=0&startpage=185 
• Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR741185, http://books.google.com/books?id=JpHjkhFLfpgC  Reprinted by Dover, 2005