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On a generalization of duality triads

100%

Schork M.

Open Mathematics

2006

tom 4

nr 2

304-318

Some aspects of duality triads introduced recently are discussed. In particular, the general solution for the triad polynomials is given. Furthermore, a generalization of the notion of duality triad is proposed and some simple properties of these generalized duality triads are derived.

Duality triads of higher rank: Further properties and some examples

100%

Schork M.

Open Mathematics

2006

tom 4

nr 3

507-524

It is shown that duality triads of higher rank are closely related to orthogonal matrix polynomials on the real line. Furthermore, some examples of duality triads of higher rank are discussed. In particular, it is shown that the generalized Stirling numbers of rank r give rise to a duality triad of rank r.

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

84%

Wituła R., Słota D.

Open Mathematics

2006

tom 4

nr 3

531-546

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.

Ograniczanie wyników

3 Open Mathematics

2 Schork M.

1 Słota D.

1 Wituła R.

3 2006

Wyniki wyszukiwania

On a generalization of duality triads

Duality triads of higher rank: Further properties and some examples

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