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A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers

Kim Taekyun, Kim Hye Kyung

Demonstratio Mathematica

2024

Vol. 57, nr 1

art. no. 20240065

In this study, we introduce the λ-analogue of Lah numbers and λ-analogue of r-Lah numbers in the view of degenerate version, respectively. We investigate their properties including recurrence relation and several identities of λ-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 λ-analogue of Lah numbers and λ-analogue of r-Lah numbers, respectively.