TY - JOUR
AU - Il`inskii, A.
PY - 2004/05/10
Y2 - 2024/05/19
TI - A probabilistic approach to <i>q</i>-polynomial coefficients, Euler and Stirling numbers. I
JF - Математическая физика, анализ, геометрия
JA - Мат. физ. анал. геом.
VL - 11
IS - 4
SE - Статті
DO -
UR - http://mag.ilt.kharkiv.ua/index.php/mag/article/view/m11-0434e
SP - 434-448
AB - 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 <i>q</i>-polynomial coefficients (in particular, with the <i>q</i>-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.
ER -