# Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

Open Mathematics (2006)

- Volume: 4, Issue: 3, page 531-546
- ISSN: 2391-5455

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topRoman Wituła, and Damian Słota. "Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences." Open Mathematics 4.3 (2006): 531-546. <http://eudml.org/doc/269281>.

@article{RomanWituła2006,

abstract = {In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.},

author = {Roman Wituła, Damian Słota},

journal = {Open Mathematics},

keywords = {11B83; 26C99; 11B39},

language = {eng},

number = {3},

pages = {531-546},

title = {Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences},

url = {http://eudml.org/doc/269281},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Roman Wituła

AU - Damian Słota

TI - Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

JO - Open Mathematics

PY - 2006

VL - 4

IS - 3

SP - 531

EP - 546

AB - In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.

LA - eng

KW - 11B83; 26C99; 11B39

UR - http://eudml.org/doc/269281

ER -

## References

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- [11] J. Morgado: “Note on the Chebyshev polynomials and applications to the Fibonacci numbers”, Portugal. Math., Vol. 52, (1995), pp. 363–378. Zbl0844.11012
- [12] S. Paszkowski: Numerical Applications of Chebyshev Polynomials and Series, PWN, Warsaw, 1975 (in Polish). Zbl0423.65012
- [13] P. Ribenboim: Fermats’s Last Theorem For Amateurs, Springer, New York 1999.
- [14] J. Riordan: “Generating functions for powers of Fibonacci numbers”, Duke Math. J., Vol. 29, (1962), pp. 5–12. http://dx.doi.org/10.1215/S0012-7094-62-02902-2 Zbl0101.28801
- [15] T. Rivlin: Chebyshev Polynomials from Approximation Theory to Algebra and Number Theory, 2nd ed., Wiley, New York, 1990. Zbl0734.41029
- [16] R. Wituła and D. Słota: “On Modified Chebyshev Polynomials”, J. Math. Anal. Appl., (2006), in print. Zbl1124.33012

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