Narumi polynomials

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

\sum_{n = 0}^{\infty} \frac{s_{n} (x)}{n!} t^{n} = {(\frac{t}{\log (1 + t)})}^{a} (1 + t)^{x} .

They form the Sheffer sequence for

g (t) = (\frac{e^{t} - 1}{t})^{- a}, f (t) = e^{t} - 1.

References

↑ Narumi, S. (1929), "On a power series having only a finite number of algebraico logarithmic singularities on its circle of convergence.", Tôhoku Mathematical Journal, 30: 185–201, JFM 55.0185.03
↑ Boas, Ralph P.; Buck, R. Creighton (1964) [1958]. Polynomial Expansions of Analytic Functions. Ergebnisse der Mathematik und ihrer Grenzgebiete. 1. Folge. Vol. 19 (2nd ed.). Springer Berlin, Heidelberg. ISBN 978-3-662-23179-1. MR 0094466. {{cite book}}: ISBN / Date incompatibility (help)
↑ Roman, Steven (1984). The Umbral Calculus. London: Academic Press. ISBN 978-0-08-087430-2.

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