A probabilistic approach to q-polynomial coefficients, Euler and Stirling numbers. I

Анотація

It is known that Bernoulli scheme of independent trials with two out- comes is connected with the binomial coefficients. The aim of this paper is to indicate stochastic processes which are connected with the q-polynomial coefficients (in particular, with the q-binomial coefficients, or the Gaussian polynomials), Stirling numbers of the first and the second kind, and Euler numbers in a natural way. A probabilistic approach allows us to give very simple proofs of some identities for these coefficients.