Gould polynomials explained

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

\displaystyle \exp(x f ^{-1} (t)) = \sum ^{inf ty} _{n =0} G _{n(x;a,b) (t ^{n})/(n!)} wheref(t) = e ^{at} (e ^{bt} -1 ) so f ^{-1} (t) = (1)/(b) \sum ^{inf ty} _{k =1} \binom{ - (b + ak)/b}{k -1 } (t ^{k})/(k)

References

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