Hankel transform of linear combination of three consecutive Catalan numbers

Radica Bojičić; M.d. Petković; Paul Barry

Article Details

Hankel transform of linear combination of three consecutive Catalan numbers

Authors:

Radica Bojičić | M.d. Petković | Paul Barry

Publisher:

Hacettepe University

Main Topics:

Algebra and Number Theory

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1470-1478

Document Type:

Article

Publication Date:

8/2025

Document Language:

English

Document ID (Org No.):

2001356972

pISSN:

2651-477X

Keywords:

Abstract:

 In this paper, we consider the Hankel determinants of the linear combination of three consecutive Catalan numbers, and then three consecutive shifted Catalan numbers. For their computing, we apply known methods based on the connections between continued fractions, orthogonal polynomials and moment-determinants. The properties of orthogonal polynomials enable us to evaluate the generating function of the corresponding sequence Hankel determinants in closed form.

 In this paper, we consider the Hankel determinants of the linear combination of three consecutive Catalan numbers, and then three consecutive shifted Catalan numbers. For their computing, we apply known methods based on the connections between continued fractions, orthogonal polynomials and moment-determinants. The properties of orthogonal polynomials enable us to evaluate the generating function of the corresponding sequence Hankel determinants in closed form.

 In this paper, we consider the Hankel determinants of the linear combination of three consecutive Catalan numbers, and then three consecutive shifted Catalan numbers. For their computing, we apply known methods based on the connections between continued fractions, orthogonal polynomials and moment-determinants. The properties of orthogonal polynomials enable us to evaluate the generating function of the corresponding sequence Hankel determinants in closed form.

 In this paper, we consider the Hankel determinants of the linear combination of three consecutive Catalan numbers, and then three consecutive shifted Catalan numbers. For their computing, we apply known methods based on the connections between continued fractions, orthogonal polynomials and moment-determinants. The properties of orthogonal polynomials enable us to evaluate the generating function of the corresponding sequence Hankel determinants in closed form.

Article Details

Hankel transform of linear combination of three consecutive Catalan numbers

Authors: Radica Bojičić | M.d. Petković | Paul Barry

Publisher: Hacettepe University

Main Topics: Algebra and Number Theory

Journal: Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1470-1478

Document Type: Article

Publication Date: 8/2025

Document Language: English

Document ID (Org No.): 2001356972

pISSN: 2651-477X

Catalan numbers

shifted Catalan numbers

Hankel transform

orthogonal polynomials

Issues

Authors:

Radica Bojičić | M.d. Petković | Paul Barry

Publisher:

Hacettepe University

Main Topics:

Algebra and Number Theory

Journal:

Hacettepe Journal of Mathematics and Statistics Vol.54 Issue 4, pp.1470-1478

Document Type:

Article

Publication Date:

8/2025

Document Language:

English

Document ID (Org No.):

2001356972

pISSN:

2651-477X