Gould polynomials

In mathematics the Gould polynomials G_n(x; a,b) are polynomials introduced by H. W. Gould and named by Roman in 1984.^[1] They are given by ^[2]

${\displaystyle \displaystyle \exp(xf(t))=\sum _{n}G_{n}(x;a,b)t^{n}/n!}$

where

${\displaystyle f(t)=\sum _{k\geq 1}{\frac {1}{b}}{\binom {-(b+ak)/b}{k-1}}{\frac {t^{k}}{k!}}}$

References

1. 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 741185, Reprinted by Dover, 2005
2. Gould, H. W. (1961), "A series transformation for finding convolution identities", Duke Math. J. Volume 28, Number 2, 193-202.