Polynomials: Theory and Applications, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".

Deadline for manuscript submissions: 28 February 2025 | Viewed by 680

Special Issue Editor


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Guest Editor
Department of Mathematics, Hannam University, Daejeon 34430, Republic of Korea
Interests: numerical verification method; scientific computing; differential equations; dynamical systems; quantum calculus; special functions
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Special Issue Information

Dear Colleagues,

The importance of polynomials in the interdisciplinary field of mathematics, engineering, and science is well known. Over the past several decades, research on polynomials has been conducted extensively in many disciplines.

This Special Issue welcomes all research papers related to polynomials in mathematics, science, and industry.

Potential topics include but are not limited to the following:

  • The modern umbral calculus (binomial, Appell, and Sheffer polynomial sequences)
  • Orthogonal polynomials, matrix orthogonal polynomials, multiple orthogonal polynomials
  • Matrix and determinant approach to special polynomial sequences
  • Applications of special polynomial sequences
  • Number theory and special functions
  • Asymptotic methods in orthogonal polynomials
  • Fractional calculus and special functions
  • Symbolic computations and special functions
  • Applications of special functions to statistics, physical sciences, and engineering.

Prof. Dr. Cheon-Seoung Ryoo
Guest Editor

Manuscript Submission Information

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Keywords

  • umbral calculus
  • orthogonal polynomials
  • matrix orthogonal polynomials
  • special polynomial sequences
  • applications of special polynomial sequences
  • number theory and special functions
  • fractional calculus and special functions
  • symbolic computations and special functions
  • applications of special functions to statistics, physical sciences, and engineering

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Published Papers (2 papers)

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Research

11 pages, 453 KiB  
Article
On Polar Jacobi Polynomials
by Roberto S. Costas-Santos
Mathematics 2024, 12(17), 2767; https://doi.org/10.3390/math12172767 - 6 Sep 2024
Viewed by 237
Abstract
In the present work, we investigate certain algebraic and differential properties of the orthogonal polynomials with respect to a discrete–continuous Sobolev-type inner product defined in terms of the Jacobi measure. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications, 2nd Edition)
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15 pages, 292 KiB  
Article
Generating Functions for Binomial Series Involving Harmonic-like Numbers
by Chunli Li and Wenchang Chu
Mathematics 2024, 12(17), 2685; https://doi.org/10.3390/math12172685 - 29 Aug 2024
Viewed by 293
Abstract
By employing the coefficient extraction method, a class of binomial series involving harmonic numbers will be reviewed through three hypergeometric F12(y2)-series. Numerous closed-form generating functions for infinite series containing binomial coefficients and harmonic numbers will be [...] Read more.
By employing the coefficient extraction method, a class of binomial series involving harmonic numbers will be reviewed through three hypergeometric F12(y2)-series. Numerous closed-form generating functions for infinite series containing binomial coefficients and harmonic numbers will be established, including several conjectured ones. Full article
(This article belongs to the Special Issue Polynomials: Theory and Applications, 2nd Edition)
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