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Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials

Publication ,  Journal Article
Dilcher, K; Jiu, L
Published in: Journal of Mathematical Analysis and Applications
May 1, 2021
Published version (DOI)

Using continued fraction expansions of certain polygamma functions as a main tool, we find orthogonal polynomials with respect to the odd-index Bernoulli polynomials B2k+1(x) and the Euler polynomials E2k+ν(x), for ν=0,1,2. In the process we also determine the corresponding Jacobi continued fractions (or J-fractions) and Hankel determinants. In all these cases the Hankel determinants are polynomials in x which factor completely over the rationals.

Duke Scholars

Lin Jiu
Author Lin Jiu DKU Faculty

Published In

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2020.124855

EISSN

1096-0813

ISSN

0022-247X

Publication Date

May 1, 2021

Volume

497

Issue

1

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics
 

Citation

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Dilcher, K., & Jiu, L. (2021). Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials. Journal of Mathematical Analysis and Applications, 497(1). https://doi.org/10.1016/j.jmaa.2020.124855
Dilcher, K., and L. Jiu. “Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials.” Journal of Mathematical Analysis and Applications 497, no. 1 (May 1, 2021). https://doi.org/10.1016/j.jmaa.2020.124855.
Dilcher K, Jiu L. Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials. Journal of Mathematical Analysis and Applications. 2021 May 1;497(1).
Dilcher, K., and L. Jiu. “Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials.” Journal of Mathematical Analysis and Applications, vol. 497, no. 1, May 2021. Scopus, doi:10.1016/j.jmaa.2020.124855.
Dilcher K, Jiu L. Orthogonal polynomials and Hankel determinants for certain Bernoulli and Euler polynomials. Journal of Mathematical Analysis and Applications. 2021 May 1;497(1).
Journal cover image

Published In

Journal of Mathematical Analysis and Applications

DOI

10.1016/j.jmaa.2020.124855

EISSN

1096-0813

ISSN

0022-247X

Publication Date

May 1, 2021

Volume

497

Issue

1

Related Subject Headings

  • General Mathematics
  • 4904 Pure mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0906 Electrical and Electronic Engineering
  • 0102 Applied Mathematics
  • 0101 Pure Mathematics