#####
Séminaire Lotharingien de Combinatoire, B30h (1993).

[Formerly: Publ. I.R.M.A. Strasbourg, 1993, 1993/034, p.
111-114.]

# Don Rawlings

# Probabilistic Interpretations of *q*-Analogues

**Abstract.**
In some instances, the parameter *q* of a *q*-analogue may
be directly identified as the probability of tails occurring
in a Bernoulli trials scheme. The simple coin-tossing game
presented in the next section gives rise to a
*q*-analogue of a standard limit formula for the
exponential function and to a *q*-analogue of Euler's
product formula for the Riemann zeta function. The context in
which these *q*-identities arise bears some resemblance
to the one Gilbert Labelle used in obtaining a
*q*-analogue of Euler's gamma function. Slight variations
of the same game also lead to probabilistic interpretations of
the inversion number and of the major index.

This paper is a summary of:

Bernoulli trials and permutation
statistics, *Internat. J. Math. Math. Sci.* **15** (1992),
291--311

Bernoulli trials and number theory, *Amer. Math. Monthly* **101** (1994),
948--952.