A family of sequences of binomial type

Abstract

For delta operator $aD-b{D}^{p+1}$ we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case $D-\frac{1}{2}{D}^2$ we show that the corresponding Bessel-Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions ${\nu }_t$, $t>0$, for which $\left\{y_n(t)\right\}$, the Bessel polynomials at $t$, is the moment sequence.

arXiv comment7 pages