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

where

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

References

↑ 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
↑ Gould, H. W. (1961), "A series transformation for finding convolution identities", Duke Math. J. Volume 28, Number 2, 193-202.

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