Fibonacci and Lucas Numbers for Real Indices and Some Applications

Wituła, R.

doi:10.12693/APhysPolA.120.755

Journal

Acta Physica Polonica A

2011 | 120 | 4 | 755-758

Article title

Fibonacci and Lucas Numbers for Real Indices and Some Applications

Authors

R. Wituła

Content

Full texts:

http://przyrbwn.icm.edu.pl/APP/PDF/120/a120z4p41.pdf [remote]

Title variants

Languages of publication

Abstracts

In this paper the notion of the Fibonacci and Lucas numbers is extended onto real indices. Next, these new numbers are used for calculating real powers of certain matrices. The presented method to the extension of elements of linear recurrence sequence to real indices ought to find practical application in wide understanding metrology and medical diagnostics.

Keywords

02.10.Yn 02.10.De 02.50.Cw

Discipline

Publisher

Journal

Acta Physica Polonica A

Year

2011

Volume

120

Issue

Pages

755-758

Physical description

Dates

published

2011-10

Contributors

author

R. Wituła

Institute of Mathematics, Silesian University of Technology, Kaszubska 23, 44-100 Gliwice, Poland

References

1. R. Wituła, D. Słota, Appl. Math. Comput. 202, 348 (2008)
2. S. Rabinowitz, in: Applications of Fibonacci Numbers, Vol. 6, Eds. G.E. Bergum, A.N. Phillipou, Kluwer 1996, p. 389
3. R. Grzymkowski, R. Wituła, Calculus Methods in Algebra, Part One, WPKJS, Gliwice 2000
4. M. Catalani, 'Generalized Bivariate Fibonacci Polynomials', arXiv:math 0211366v2, 1-11 (2004)
5. M. Catalani, 'Some formulae for bivariate Fibonacci and Lucas polynomials', arXiv:math 0406323v1, 1-9 (2004)
6. X. Fu, X. Zhou, Appl. Math. Comput. 200, 96 (2008)
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8. S. Falcon, A. Plaza, Chaos Solitons Fractals 38, 409 (2008)
9. S. Falcon, A. Plaza, Chaos Solitons Fractals 38, 993 (2008)
10. M.E.H. Ismail, Fibonacci Quart. 46/47, 167 (2008/09)
11. S.P. Pethe, R.M. Fernandes, Ulam Quart. 3, 15 (1995)
12. R. Andre-Jeannin, Fibonacci Quart. 29, 13 (1991)
13. T. Pustelny, C. Tyszkiewicz, K. Barczak, Opt. Appl. 33, 469 (2003)
14. K. Barczak, T. Pustelny, D. Dorosz, J. Dorosz, Europ. Phys. J.-Special Topics 154, 11 (2008)
15. M. Gawlikowski, T. Pustelny, B. Przywara-Chowaniec, J. Nowak-Gawlikowska, Acta Phys. Pol. A 118, 1183 (2010)
16. ] P. Struk, T. Pustelny, K. Gut, K. Gołaszewska, E. Kamiń ska, M. Ekielski, I. Pasternak, E. Łusakowska, A. Piotrowska, Acta Phys. Pol. A 116, 414 (2009)
17. R. Wituła, D. Słota, Lect. Notes Comput. Sci. 5544, 580 (2009)

Document Type

Publication order reference

Identifiers

DOI

10.12693/APhysPolA.120.755

YADDA identifier

bwmeta1.element.bwnjournal-article-appv120n441kz