Hankel Determinants of a Linear Combination of Three Successive Catalan Numbers

Bouras, B.

doi:10.1007/s00009-012-0200-x

Cited by 6 publications

(4 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many authors has carried out the computation of Hankel determinant of more than tow consecutives Catalan or Motzkin numbers [17,20]. It is conjectured [20] that for Catalan numbers, the Hankel transform {h n } n satisfies a homogeneous linear recurrence relation of order 2 r .…”

Section: Hankel Transforms Of Linear Combinations Of Catalan and Motzmentioning

confidence: 99%

A unified approach for the Hankel determinants of classical combinatorial numbers

Elouafi¹

2015

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Please cite this article in press as: M. Elouafi, A unified approach for the Hankel determinants of classical combinatorial numbers, J. Math. Anal. Appl. (2015), http://dx.Abstract. We give a general formula for the determinants of a class of Hankel matrices which arise in combinatorics theory. We revisit and extend existant results on Hankel determinants involving the sum of consecutive Catalan, Motzkin and Schroder numbers and we prove a conjecture in [20] about the recurrence relations satisfied by the Hankel transform of linear combinations of Catalans numbers.

show abstract

Section: Hankel Transforms Of Linear Combinations Of Catalan and Motzmentioning

confidence: 99%

A unified approach for the Hankel determinants of classical combinatorial numbers

Elouafi¹

2015

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

show abstract

“…In the last few years investigation of the Hankel determinant gained much attention and brief survey of those work until 2013 can be found in the introduction of the paper [24]. Much recent history of development in this direction can be found in [1,3,4,7,9,13,16,26,31]. Wide variety of applications of Toeplitz-plus-Hankel systems arise in linear filtering theory, discrete inverse scattering, and discretization of certain integral equations arising in mathematical physics [30].…”

Section: Introductionmentioning

confidence: 99%

Hermitian–Toeplitz determinants for functions with bounded turning

Kumar¹,

Cho²

2021

Turk J Math

View full text Add to dashboard Cite

There is a rich literature on estimation of second and third Hankel determinants for normalised analytic functions in geometric function theory. It is also, therefore, natural to explore the concept of the Hermitian-Toeplitz determinants for such functions. In this paper, the sharp lower and upper estimations for third-order Hermitian-Toeplitz determinant for functions with bounded turning of order α , are obtained.

show abstract

“…Bouras [7] considered the determinant of H m (z) where z = (z n ) n≥0 is defined as a linear combination of three successive shifted Catalan numbers…”

Section: Introductionmentioning

confidence: 99%

“…There exists an monic OPS, {P n (x)} n≥0 , with respect to positive-definite L y ;(7) There exist constants σ = (s k ) k≥0 and τ = (t k ) k≥1 with t k > 0 satisfying (2.2);(8) There exist constants σ = (s k ) k≥0 and τ = (t k ) k≥1 with t k > 0 satisfying (1.3); (9) There exists a positive-definite Riesz functional L y satisfying (2.5). Proof.…”

mentioning

confidence: 99%