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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 33, Fasc. 2,
pages 401 - 408
 

A FAMILY OF SEQUENCES OF BINOMIAL TYPE

Wojciech Młotkowski
Anna Romanowicz

Abstract: For a delta operator aD - bDp+1  we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D - 1D2
    2  we show that the corresponding Bessel–Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions. We also find probability distributions ν
 t  , t > 0 , for which (y (t))
 n , the Bessel polynomials at t , 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.

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