Polynomial Sequences and Their Applications, 2nd Edition

Dear colleagues,

Weierstrass’s Approximation Theorem (1885) is one of the most popular, fundamental, practically important and frequently used theorems in approximation theory. It asserts that every continuous function defined on a closed interval can be uniformly approximated by polynomials. Polynomials are incredibly useful mathematical tools, as they are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. Therefore, sequences of polynomials perform an important role in several branches of science: mathematics, physics, engineering, etc. For example, polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equations. Among these, we highlight orthogonal polynomials. In statistics, Hermite polynomials are very important, and they are also orthogonal polynomials. In algebra and combinatorics, umbral polynomials are used, such as rising factorials, falling factorials and Abel, Bell, Bernoulli, Euler, Boile, ciclotomic, Dickson, Fibonacci, Lucas and Touchard polynomials. Some of these belong to special classes, such as Sheffer, Appell and binomial types. For this reason, research in this field appears in different journals/magazines.

A Special Issue that compiles the state of the art of current research will be very useful for the mathematical community.

 Potential topics include but are not limited to the following:

• Modern umbral calculus (binomial, Appell and Sheffer polynomial sequences)
• Orthogonal polynomials, matrix orthogonal polynomials, multiple orthogonal polynomials and orthogonal polynomials of several variables
• Operational methods and the monomiality principle
• Generating functions of special classes
• Matrix and determinant approach to special polynomial sequences
• Applications of special polynomial sequences in approximation theory, in boundary value problems and in quadrature formulas
• Number theory and special classes of polynomials
• Asymptotic methods in orthogonal polynomials
• Fractional calculus
• Bernstein basis
• Extrapolation methods

Prof. Dr. Francesco Aldo Costabile
Prof. Dr. Maria I. Gualtieri
Prof. Dr. Anna Napoli
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• orthogonal polynomials
• matrix methods
• monomiality principle
• generating functions
• Sheffer, Appell and binomial classes
• Lidstone type class
• umbral calculus
• interpolation
• boundary value problems
• numerical quadrature

• Polynomial Sequences and Their Applications in Mathematics (16 articles)