A generalization of André-Jeannin’s symmetric identity
Copyright policy )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.
combinatorial sums; sums of reciprocals; three-term recurrences; q-Fibonacci polynomials; q-Fibonacci numbers; q-Lucas polynomials; q-Lucas numbers; q-Pell polynomials; q-Pell numbers; q-Jacobsthal polynomials; q-Jacobsthal numbers; q-Chebyshev polynomials; q-Morgan-Voyce polynomials, General Medicine
combinatorial sums; sums of reciprocals; three-term recurrences; q-Fibonacci polynomials; q-Fibonacci numbers; q-Lucas polynomials; q-Lucas numbers; q-Pell polynomials; q-Pell numbers; q-Jacobsthal polynomials; q-Jacobsthal numbers; q-Chebyshev polynomials; q-Morgan-Voyce polynomials, General Medicine
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