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

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

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

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, MR 0094466
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
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, MR 0741185 Reprinted by Dover, 2005

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