Two new trigonometric formulas with applications. (English) Zbl 0711.33004
Let \(T_ n(x)\) and \(U_ n(x)\) be the Chebyshev polynomials of the first and second kinds. The author derives the expansion of \(T_{n-k}(x)\) in terms of \(x^{n+k-2m}T_{2m}(x)\) and of \(U_{n-k-1}(x)\) in terms of \(x^{n+k-2m}U_{2m-1}(x)\).
Reviewer: D.M.Bressoud
MSC:
| 33C45 | Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) |
Keywords:
Chebyshev polynomialsReferences:
| [1] | Byrd, P. F., Expansion of Analytic Functions in Terms Involving Lucas Numbers and Similar Number Sequences, Fibonacci Quarterly, 3, 101-114 (1965) · Zbl 0278.33016 |
| [2] | Magnus, W.; Oberhettinger, F.; Soni, R. P., Formulas and Theorems for the Special Functions of Mathematical Physics (1966), Springer-Verlag: Springer-Verlag New York · Zbl 0143.08502 |
| [3] | Riordan, J., Combinatorial Identities (1968), Wiley: Wiley New York · Zbl 0194.00502 |
| [4] | Rung, D. C.; Obaid, S. A., Combinatorics and Flexure, J. Appl. Math. Phys., 36, 443-459 (1985) · Zbl 0627.73020 |
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