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Approach of q-Derivative Operators to Terminating q-Series Formulae

Abstract

The q-derivative operator approach is illustrated by reviewing several typical summation formulae of terminating basic hypergeometric series.

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A generalization of André-Jeannin’s symmetric identity

Abstract

In 1997, Richard André-Jeannin obtained a symmetric identity involving the reciprocal of the Horadam numbers Wn, defined by a three-term recurrence Wn +2 = P Wn +1 − QWn with constant coefficients. In this paper, we extend this identity to sequences {an}n ∈ℕ satisfying a three-term recurrence an +2 = pn +1 an +1 + qn +1 an with arbitrary coefficients. Then, we specialize such an identity to several q-polynomials of combinatorial interest, such as the q-Fibonacci, q-Lucas, q-Pell, q-Jacobsthal, q-Chebyshev and q-Morgan-Voyce polynomials.

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