Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials (Q1996148)
From MaRDI portal
| This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials |
scientific article |
Statements
Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials (English)
0 references
3 March 2021
0 references
The purpose of this paper is to prove certain properties of Hankel determinants for Bernoulli and Euler polynomials by using recurrences, continued fractions and a kind of umbral calculus. First, several well-known results for Hankel determinants, orthogonal polynomials and continued fractions are restated. Then the concepts even ann odd canonical contraction of a continued fraction are defined. In the following, the Bernoulli polynomial case with the polygamma function and the Euler polynomial case according to \textit{W. A. Al-Salam} and \textit{L. Carlitz} [Port. Math. 18, 91--99 (1959; Zbl 0093.01504)] with monic orthogonal polynomials are considered. The main results here are for even-index polynomials or odd-index polynomials. The proof uses Laplace transform. Finally, shifted sequences are considered. Misprint in 1.3 (1).
0 references
Bernoulli polynomial
0 references
Euler polynomial
0 references
Hankel determinant
0 references
orthogonal polynomial
0 references
continued fraction
0 references
polygamma function
0 references
0 references
0 references
0.93386364
0 references
0.92463523
0 references
0.9230763
0 references
0.9178431
0 references
0.9152111
0 references
0.9141508
0 references
0 references
0 references
0.90523547
0 references