A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers - Kim Taekyun; Kim Hye Kyung (Demonstratio Mathematica)
In this study, we introduce the λλ -analogue of Lah numbers and λλ -analogue of rr-Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of λλ -analogue of Lah numbers arising from degenerate differential operators. Using these new identities, we study the normal ordering of degenerate integral power of the number operator in terms of boson operators, which is represented by means of λλ -analogue of Lah numbers and λλ -analogue of rr-Lah numbers, respectively.