Abstract:
The author's previous work provided a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years. Its numerous applications in various areas of mathematics, physics, and other fields were described, and an extensive bibliography was presented. This work overviews the studies not covered in the previous one and addresses new results published in many monographs and journals. Additionally, results concerning the estimation of zeros of some special polynomials and functions closely related to the Rayleigh function are described. The overview embraces the issues addressed in the scientific literature up to the last years.
Key words:Rayleigh special function, overview of new results related to the Rayleigh function, Lommel polynomials, estimates for zeros of Bessel functions, orthogonal polynomials.
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