Ma's identity and its application

Roman Wituła, Edyta Hetmaniok, Damian Słota

Abstract


In the paper we distinguish the, so called, Ma's polynomials and we introduce connections of these polynomials with the classic Cauchy polynomials and the Ferrers-Jackson's polynomials. Presented connections enable to receive certain interesting divisibility relations for all these three types of polynomials and some other symmetric polynomials. Application of the discussed identities for determining the limits of quotients of the respective polynomials in two variables are also presented here.

Keywords


Ma's polynomials; Cauchy polynomials; Ferrers-Jackson's polynomials

Mathematics Subject Classification


11B39; 12D05

References


Ma, X. "A generalization of the Kummer identity and its application to Fibonacci-Lucas sequences." Fibonacci Quart. 36 (1998): 339-347.

Ribenboim, P. "Fermat’s Last Theorem for Amateurs." New York: Springer-Verlag, 1999.

Wituła, R. and D. Słota. "Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences." Centr. Eur. J. Math. 4 (2006): 531-546.

Hoggatt, Jr., V.E. and M. Bicknell. "Roots of Fibonacci Polynomials." Fibonacci Quart. 11 (1973): 271-274.


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