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Some identities involving special numbers and moments of random variables. (English) Zbl 1418.05022
Summary: In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here, the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-order Bernoulli numbers and Bernoulli numbers of the second kind.

MSC:
 05A19 Combinatorial identities, bijective combinatorics 11B83 Special sequences and polynomials
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References:
 [1] L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Util. Math. 15 (1979), 51-88. · Zbl 0404.05004 [2] —-, Generalized Stirling and related numbers, Riv. Mat. Univ. Parma 4 (1979), 79-99. · Zbl 0402.10011 [3] —-, The number of derangements of a sequence with given specification, Fibonacci Quart. 16 (1978), 255-258. · Zbl 0403.05008 [4] L. Comtet, Advanced combinatorics, The art of finite and infinite expansions, D. Reidel Publishing Co., Dordrecht, 1974. · Zbl 0283.05001 [5] D.S. Kim and T. Kim, Some $$p$$-adic integral on $$\Bbb Z_p$$ associated with trigonometric functions, Russian J. Math. Phys. 25 (2018), 300-308. · Zbl 1433.11133 [6] T. Kim, A note on degenerate Stirling polynomials of the second kind, Proc. Jangjeon Math. Soc. 20 (2017), 319-331. · Zbl 1377.11027 [7] —-, $$\lambda$$-analogue of Stirling numbers of the first kind, Adv. Stud. Contemp. Math. (Kyungshang) 27 (2017), 423-429. · Zbl 1420.11050 [8] T. Kim and D.S. Kim, Some identities on derangement and degenerate derangement polynomials, arXiv:1712.03397, 2017. · Zbl 1414.11036 [9] S. Roman, The umbral calculus, Pure Appl. Math. 111 (1984). [10] S.M. Ross, Introduction to probability and statistics for engineers and scientists, Harcourt/Academic Press, Burlington, MA, 2000. · Zbl 0942.62001 [11] Y. Simsek, Identities on the Changhee numbers and Apostol-type Daehee polynomials, Adv. Stud. Contemp. Math. (Kyungshang) 27 (2017), 199-212. · Zbl 1371.11060 [12] S. Ping and W. Tianming, Probabilistic representations of Stirling numbers with applications, Acta Math. Sinica 41 (1998), 281-290. · Zbl 1015.05008
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