Steady-state Markov chain models for the Heine and Euler distributions

Abstract

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Convergence properties of the q-deformed binomial distribution

“…For properties and applications of this distribution we refer to Johnson, Kemp and Kotz [12], Benkherouf and Bather [1], Biedenharn [2], Kemp [13,14,16], Charalambides and Papadatos [4] and Ostrovska [19,20].…”

q-SERIES IN MARKOV CHAINS WITH BINOMIAL TRANSITIONS

“…There exists a rich theory for the class of q-hypergeometric series and their q-calculus, which enables fast calculations and simplifications. In the queuing theory literature there exist only a few articles in which this theory has been applied (see, e.g., Ismail [16], Kemp [18][19][20], and Kemp and Newton [21]). For this reason and for the sake of self-completeness, we will briefly summarize the basic definitions and results of this theory.…”