  In this paper, a q-analogue of r-Whitney-Lah numbers, also known as
(q,r)-Whitney-Lah number, denoted by $L_{m,r}[n,k]_q$ is defined using the
triangular recurrence relation. Several fundamental properties for the
q-analogue are established such as vertical and horizontal recurrence
relations, horizontal and exponential generating functions. Moreover, an
explicit formula for (q,r)-Whitney-Lah number is derived using the concept of
q-difference operator, particularly, the q-analogue of Newton's Interpolation
Formula (the umbral version of Taylor series). Furthermore, an explicit formula
for the first form (q,r)-Dowling numbers is obtained which is expressed in
terms of (q,r)-Whitney-Lah numbers and (q,r)-Whitney numbers of the second
kind.
