A FAMILY OF SEQUENCES OF BINOMIAL TYPE
Wojciech Młotkowski
Anna Romanowicz
Abstract: For a delta operator we find the corresponding polynomial sequence of
binomial type and relations with Fuss numbers. In the case of we show that
the corresponding Bessel–Carlitz polynomials are moments of the convolution
semigroup of inverse Gaussian distributions. We also find probability distributions ,
, for which , the Bessel polynomials at , is the moment sequence.
2000 AMS Mathematics Subject Classification: Primary: 05A40; Secondary: 60E07,
44A60.
Keywords and phrases: Sequence of binomial type, Bessel polynomials, inverse
Gaussian distribution.