@article{Explicit Formulas for the First Form (q,r)-Dowling Numbers and (q,r)-Whitney-Lah Numbers_2021, place={Maryland, USA}, volume={14}, url={https://www.ejpam.com/index.php/ejpam/article/view/3900}, DOI={10.29020/nybg.ejpam.v14i1.3900}, abstractNote={
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.
}, number={1}, journal={European Journal of Pure and Applied Mathematics}, year={2021}, month={Jan.}, pages={65–81} }