第一形式（q，r）-Dowling数和（q，r）-Whitney-Lah数的显式公式
Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers
摘要：
利用三角递归关系定义了r-Whitney-Lah数的一个q-模拟，也称为（q，r）-Whitney-Lah数，记作$L_{m,r}[n,k]_q$.建立了q模拟的几个基本性质，如垂直和水平递归关系，水平和指数母函数。此外，利用q-差分算子的概念，特别是牛顿插值公式（泰勒级数的本影形式）的q-模拟，导出了（q，r）-Whitney-Lah数的一个显式公式.进一步，得到了第一种形式（q，r）-Dowling数的一个显式公式，该公式用（q，r）-Whitney-Lah数和第二类（q，r）-Whitney数表示.
英文摘要：
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.
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