Submission Deadline: 31 December 2021 (closed)
The computers began to appear in the 1950s, and often incorrect, estimations were done related to the impact of these devices on applied mathematics, science and engineering. One of these estimations was that the need for special functions, or higher transcendental functions (as they are also known), would disappear entirely. This was based on the observation that the key use of these functions in those days was to approximate the solutions of classical differential (or partial differential) equations: with the mathematical software it would become possible to solve these equations by direct numerical methods. This observation is in fact correct; even so, a study of current computational journals in the sciences reveals a continuous need for numerical algorithms to generate Airy functions, Bessel functions, Coulomb wave functions, error functions and exponential integrals, etc.
This special issue focuses on the applications and computer modeling of the special functions and polynomials to various areas of mathematics. Thorough knowledge of special functions is required in modern engineering, physical science applications and computer modeling. These functions typically arise in such applications as communications systems, statistical probability distribution, electro-optics, nonlinear wave propagation, electromagnetic theory, potential theory, electric circuit theory, and quantum mechanics.
Potential topics include but are not limited to the following:
• Computer modeling of Special functions and polynomials
• Analytical properties and applications of Special functions.
• Inequalities for Special Functions
• Integration of products of Special Functions
• Properties of ordinary and general families of Special Polynomials
• Operational techniques involving Special Polynomials
• Classes of mixed Special Polynomials and their properties
• Other miscellaneous applications of Special Functions and Special Polynomials
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