A family of sequences of binomial type

• Autorzy: Młotkowski W. , Romanowicz A.
• Języki publikacji: EN

Abstrakty

EN

For a delta operator aD – bD^p+1 we find the corresponding polynomial sequence of binomial type and relations with Fuss numbers. In the case of D – 1/2D² we show that the corresponding Bessel-Carlitz polynomials are moments of the convolution semigroup of inverse Gaussian distributions.We also find probability distributions v_t, t > 0, for which {y_n(t)}, the Bessel polynomials at t, is the moment sequence.

Słowa kluczowe

EN

sequence of binomial type; Bessel polynomials; inverse Gaussian distribution

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 401--408
• Opis fizyczny: Bibliogr. 12 poz., rys.

Twórcy

autor

Młotkowski W.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

autor

Romanowicz A.

• Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• [1] N. Balakrishnan and V. B. Nevzorov, A Primer on Statistical Distributions, Wiley, Hoboken, New Jersey, 2003.
• [2] S. Bouroubi and M. Abbas, New identities for Bell polynomials, Rostock. Math. Kolloq. 61 (2006), pp. 49-55.
• [3] L. Carlitz, A note on the Bessel polynomials, Duke Math. J. 24 (2) (1957), pp. 151-162.
• [4] R. L. Graham, D. E. Knuth, and O. Patashnik, Concrete Mathematics. A Foundation for Computer Science, Addison-Wesley, New York 1994.
• [5] E. Grosswald, Bessel Polynomials, Lecture Notes in Math., Vol. 698, Springer, New York 1978.
• [6] T.-X. He, L. C. Hsu, and P. J.-S. Shiue, Symbolization of generating functions; an application of the Mullin-Rota theory of binomial enumeration, Comput. Math. Appl. 54 (2007), pp. 664-678.
• [7] H. L. Krall and O. Frink, A new class of orthogonal polynomials: The Bessel polynomials, Trans. Amer. Math. Soc. 65 (1) (1948), pp. 100-115.
• [8] M. Mihoubi, Bell polynomials and binomial type sequences, Discrete Math. 308 (2008), pp. 2450-2459.
• [9] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, NIST Handbook of Mathematical Functions, Cambridge University Press, Cambridge 2010.
• [10] S. Roman, The Umbral Calculus, Academic Press, 1984.
• [11] N. J. A. Sloane, The On-Line Encyclopedia of Integer Sequences, 2013, http://oeis.org/.
• [12] F. W. Steutel and K. van Harn, Infinite Divisibility of Probability Distributions on the Real Line, Marcel Dekker, 2004.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).