Polynomial Sequences and Their Applications, 2nd Edition
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Computational and Applied Mathematics".
Deadline for manuscript submissions: 25 June 2025 | Viewed by 599
Special Issue Editors
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
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. Maria I. Gualtieri
Dr. Anna Napoli
Guest Editors
Manuscript Submission Information
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Keywords
- orthogonal polynomials
- matrix methods
- monomiality principle
- generating functions
- Sheffer, Appell and binomial classes
- Lidstone type class
- umbral calculus
- interpolation
- boundary value problems
- numerical quadrature
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Related Special Issue
- Polynomial Sequences and Their Applications in Mathematics (16 articles)
