Airy Functions Demystified - III: A Fresh Look at the Relation Between Airy and Bessel Functions

Resonance

article

M S Ramkarthik¹  Elizabeth Louis Pereira¹ 

[1] Department of Physics Visvesvaraya National Institute of Technology Nagpur 440 010

关键词: Airy function;    Bairy function;    Bessel functions;    modified Bessel functions;    Macdonald function;    asymptotic expansions;    convergent series.;   

DOI  :  10.1007/s12045-022-1514-z

学科分类：社会科学、人文和艺术（综合）

来源: Springer

【 摘 要 】

Airy and Bessel functions are one of the most popular andimportant 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 bya number of assumptions, approximations, and sometimeseven misconceptions. This motivated us to develop a freshand transparent method to establish these relations. As thecontinuation 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.

【 授权许可】

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