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Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 9, Pages 1387–1441 (Mi zvmmf10084)  

This article is cited in 9 scientific papers (total in 9 papers)

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

M. K. Kerimov

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

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.

Key words: Bessel functions, real zeros of Bessel functions, research and computation techniques.

DOI: https://doi.org/10.7868/S0044466914090087

Full text: PDF file (2114 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2014, 54:9, 1337–1388

Bibliographic databases:

UDC: 519.65
Received: 14.04.2014

Citation: M. K. Kerimov, “Studies on the zeros of Bessel functions and methods for their computation”, Zh. Vychisl. Mat. Mat. Fiz., 54:9 (2014), 1387–1441; Comput. Math. Math. Phys., 54:9 (2014), 1337–1388

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. E. S. Kozlova, V. V. Kotlyar, S. A. Degtyarev, “Modelirovanie rezonansnoi fokusirovki pikosekundnogo impulsa dielektricheskim mikrotsilindrom”, Kompyuternaya optika, 39:1 (2015), 45–51  mathnet  crossref
    2. M. K. Kerimov, “Studies on the zeros of Bessel functions and methods for their computation: 2. Monotonicity, convexity, concavity, and other properties”, Comput. Math. Math. Phys., 56:7 (2016), 1175–1208  mathnet  crossref  crossref  isi  elib
    3. M. K. Kerimov, “Studies on the zeros of Bessel functions and methods for their computation: 3. Some new works on monotonicity, convexity, and other properties”, Comput. Math. Math. Phys., 56:12 (2016), 1949–1991  mathnet  crossref  crossref  isi  elib
    4. S. S. Budzinskiy, D. M. Kharitonov, “On inflection points of Bessel functions of the second kind of positive order”, Integral Transform. Spec. Funct., 28:12 (2017), 909–914  crossref  mathscinet  zmath  isi  scopus
    5. A. Baricz, Ch. G. Kokologiannaki, T. K. Pogany, “Zeros of Bessel function derivatives”, Proc. Amer. Math. Soc., 146:1 (2018), 209–222  crossref  mathscinet  zmath  isi  scopus
    6. M. K. Kerimov, “Studies on the zeroes of Bessel functions and methods for their computation: IV. Inequalities, estimates, expansions, etc., for zeros of Bessel functions”, Comput. Math. Math. Phys., 58:1 (2018), 1–37  mathnet  crossref  crossref  isi  elib
    7. Bobkov V., “Asymptotic Relation For Zeros of Cross-Product of Bessel Functions and Applications”, J. Math. Anal. Appl., 472:1 (2019), 1078–1092  crossref  isi
    8. A. A. Gimaltdinova, E. P. Anosova, “O nulyakh kombinatsii proizvedenii funktsii Besselya”, Vestn. Tomsk. gos. un-ta. Matem. i mekh., 2019, no. 60, 5–10  mathnet  crossref  elib
    9. A. V. Glushak, “Uniqueness Criterion for the Solution of Boundary-Value Problems for the Abstract Euler–Poisson–Darboux Equation on a Finite Interval”, Math. Notes, 109:6 (2021), 867–875  mathnet  crossref  crossref  isi  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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