Abstract
Airy and Bessel functions are one of the most popular and important special functions in various branches of physics, mathematics, and engineering. An observation to their behavior for the real argument suggest that they are related. This relation was studied earlier, but were accompanied by a number of assumptions, approximations, and sometimes even misconceptions. This motivated us to develop a fresh and transparent method to establish these relations. As the continuation of our study of the two papers published in resonance already, here we have used the general asymptotic series and the convergent series of these functions and thereby developed two new methods which throw light on the subtle interrelationships between these functions. Numerical evidences of our claims are provided for better clarity and understanding.
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M S Ramkarthik (left) is an Assistant Professor at the Department of Physics, Visvesvaraya National Institute of Technology, Nagpur. He is working in the field of quantum information theory, quantum computing, entanglement and mathematical physics.
Elizabeth Louis Pereira (right) is a second-year M.Sc. student working under the guidance of Dr M S Ramkarthik at the Department of Physics, Visvesvaraya National Institute of Technology, Nagpur and her interests are in theoretical and mathematical physics.
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Ramkarthik, M.S., Pereira, E.L. Airy Functions Demystified — III. Reson 27, 2213–2241 (2022). https://doi.org/10.1007/s12045-022-1514-z
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DOI: https://doi.org/10.1007/s12045-022-1514-z