A general two-term recurrence and its solution

A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials

“…Clearly the connection coefficients u(n, k) in (4.15) are characterized by the recurrence u(n, k) = u(n − 1, k − 1) + (a n−1 + b k )u(n − 1, k) with boundary conditions u(n, 0) = n−1 i=0 (a i +b 0 ) and u(0, k) = δ 0,k (the Kronecker delta function). Hence we recover the main result of Mansour et al [15] (see also [19]).…”

“…Finally, it is interesting to note that the following special case of Newton's formula (4.12) has been rediscovered recently by Mansour et al [15]. for k = 0, .…”

The translated Whitney–Lah numbers: generalizations and q-analogues

“…This may be verified by simply setting α = 1 in the defining relations of the former. Recently, Mansour et al [16] defined the recurrence relation…”

A q-analogue of α־-Whitney numbers

“…, r) the w q,m,ᾱ (n) is reduced to the r-Whitney matrix of the first kind [12]. Mansour et al [9] derived a closed formula for all sequences satisfying a certain recurrence relation as follows:…”