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Studies on the zeros of Bessel functions and methods for their computation

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Abstract

The zeros of Bessel functions play an important role in computational mathematics, mathematical physics, and other areas of natural sciences. Studies addressing these zeros (their properties, computational methods) can be found in various sources. This paper offers a detailed overview of the results concerning the real zeros of the Bessel functions of the first and second kinds and general cylinder functions. The author intends to publish several overviews on this subject. In this first publication, works dealing with real zeros are analyzed. Primary emphasis is placed on classical results, which are still important. Some of the most recent publications are also discussed.

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  1. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    M. K. Kerimov

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Original Russian Text © M.K. Kerimov, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 9, pp. 1387–1441.

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Kerimov, M.K. Studies on the zeros of Bessel functions and methods for their computation. Comput. Math. and Math. Phys. 54, 1337–1388 (2014). https://doi.org/10.1134/S0965542514090073

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