Some identities involving the \((p,q)\)-Chebyshev polynomials. (Chinese. English summary) Zbl 1349.11040
Summary: The \((p, q)\)-Chebyshev polynomials \(T_{(p, q, n)}(x)\) and \(U_{(p, q, n)}(x)\) are defined. Using the elementary method to study their properties, some relationships between Chebyshev polynomial and the generalizations of Fibonacci sequence, Lucas sequences are established. The sum convolution formulas of \(T_{(p, q, n)}(x)\) and \(U_{(p, q, n)}(x)\) are obtained.
MSC:
| 11B65 | Binomial coefficients; factorials; \(q\)-identities |
| 11B39 | Fibonacci and Lucas numbers and polynomials and generalizations |
