Add to ORKG17 pagesInternational audienceIn this paper we shall survey the various methods of evaluating Hankel determinants and as an illustration we evaluate some Hankel determinants of a q-analogue of Catalan numbers. Here we consider $\frac{(aq;q)_{n}}{(abq^{2};q)_{n}}$ as a q-analogue of Catalan numbers $C_{n}=\frac1{n+1}\binom{2n}{n}$, which is known as the moments of the little q-Jacobi polynomials. We also give several proofs of this q-analogue, in which we use lattice paths, the orthogonal polynomials, or the basic hypergeometric series. We also consider a q-analogue of Schröder Hankel determinants, and give a new proof of Moztkin Hankel determinants using an addition formula for ${}_2F_{1}$
We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determi...
Research Doctorate - Doctor of Philosophy (PhD)This thesis focuses on the application of matrix dete...
I give simple elementary proofs for some well-known Hankel determinants and their q − analogues. My ...
17 pagesInternational audienceIn this paper we shall survey the various methods of evaluating Hankel...
In this note we give a survey about polynomials whose moments are multiples of super Catalan numbers...
In a recent paper Aleksandar Cvetkovic, Predrag Rajkovic and Milos ̌ Ivkovic proved that for the Cat...
AbstractA class of numbers, called Catalan-like numbers, are introduced which unify many well-known ...
AbstractIn this paper we deal with Hankel determinants of the form det[ai+j+r(x)]i,j=0n, where r is ...
Abstract. In our previous works “Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel ...
We present two q-analogs of the super Catalan numbers, which also generalize Carlitz’s q-Catalan num...
We evaluate some Hankel determinants of Meixner polynomials, associated to the series exp( P [i]zi=i...
This note is a supplement to my paper “Some elementary results and conjectures about q Newton binom...
AbstractWe prove addition formulas for some polynomials built on combinatorial sequences (Catalan nu...
AbstractCatalan numbers are examined in the context of hypergeometric series. We are thus able to pr...
We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determi...
We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determi...
Research Doctorate - Doctor of Philosophy (PhD)This thesis focuses on the application of matrix dete...
I give simple elementary proofs for some well-known Hankel determinants and their q − analogues. My ...
17 pagesInternational audienceIn this paper we shall survey the various methods of evaluating Hankel...
In this note we give a survey about polynomials whose moments are multiples of super Catalan numbers...
In a recent paper Aleksandar Cvetkovic, Predrag Rajkovic and Milos ̌ Ivkovic proved that for the Cat...
AbstractA class of numbers, called Catalan-like numbers, are introduced which unify many well-known ...
AbstractIn this paper we deal with Hankel determinants of the form det[ai+j+r(x)]i,j=0n, where r is ...
Abstract. In our previous works “Pfaffian decomposition and a Pfaffian analogue of q-Catalan Hankel ...
We present two q-analogs of the super Catalan numbers, which also generalize Carlitz’s q-Catalan num...
We evaluate some Hankel determinants of Meixner polynomials, associated to the series exp( P [i]zi=i...
This note is a supplement to my paper “Some elementary results and conjectures about q Newton binom...
AbstractWe prove addition formulas for some polynomials built on combinatorial sequences (Catalan nu...
AbstractCatalan numbers are examined in the context of hypergeometric series. We are thus able to pr...
We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determi...
We use moment representations of orthogonal polynomials to evaluate the corresponding Hankel determi...
Research Doctorate - Doctor of Philosophy (PhD)This thesis focuses on the application of matrix dete...
I give simple elementary proofs for some well-known Hankel determinants and their q − analogues. My ...