TY - JOUR
TI - Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers
PY - 2021/01/31
Y2 - 2024/10/14
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 14
IS - 1
LA - en
DO - 10.29020/nybg.ejpam.v14i1.3900
UR - https://doi.org/10.29020/nybg.ejpam.v14i1.3900
SP - 65-81
AB - In this paper, aÂ q-analogue ofÂ r-Whitney-Lah numbers, also known as (q,r)-Whitney-Lah number, denoted by $L_{m,r}Â [n, k]_q$Â is defined using the triangular recurrence relation. Several fundamental properties for theÂ 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 ofÂ q-difference operator, particularly, theÂ q-analogue of Newtonâ€™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.
ER -