| Title:
|
Circulants and the factorization of the Fibonacci–like numbers (English) |
| Author:
|
Seibert, Jaroslav |
| Author:
|
Trojovský, Pavel |
| Language:
|
English |
| Journal:
|
Acta Mathematica Universitatis Ostraviensis |
| ISSN:
|
1214-8148 |
| Volume:
|
14 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
63-70 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev polynomials. In this paper some results on factorizations of the Fibonacci–like numbers $U_n$ and their squares are given. We find the factorizations using the circulant matrices, their determinants and eigenvalues. (English) |
| Keyword:
|
Fibonacci and Lucas numbers |
| Keyword:
|
tridiagonal matrix |
| Keyword:
|
circulant |
| MSC:
|
05A15 |
| MSC:
|
05A19 |
| MSC:
|
11B39 |
| idZBL:
|
Zbl 1132.11009 |
| idMR:
|
MR2298915 |
| . |
| Date available:
|
2009-12-29T09:20:41Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137485 |
| . |
| Reference:
|
[1] Cahill, N. D., D’Errico, J. R., Narayan, D. A. and Narayan, J. Y.: Fibonacci determinants.College Mathematics Journal 33.3 (2002), 221-225. |
| Reference:
|
[2] Cahill, N. D., D’Errico, J. R., Spence, J. P.: Complex factorizations of the Fibonacci and Lucas numbers.The Fibonacci Quarterly 41.1 (2003), 13-19. MR 1962276 |
| Reference:
|
[3] Cahill, N. D., Narayan, D. A.: Fibonacci and Lucas numbers as tridiagonal matrix determinants.The Fibonacci Quarterly 42.2 (2004), 216-221. MR 2093876 |
| Reference:
|
[4] Gradshteyn, J. S., Ryzhik, I. M.: Tables of Integrals, Series and Products.5th ed. San Diego, CA: Academic Press, 1979. |
| Reference:
|
[5] Horadam, A. F.: Elliptic functions and Lambert series in the summation of reciprocals in certain recurrence–generated sequences.The Fibonacci Quarterly 26.2 (1988), 98-114. Zbl 0647.10014, MR 0938583 |
| . |
