Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
Tóm tắt
Some recent works related to the Rayleigh function are analyzed that reestablish results that have been known in the literature for over one hundred years.
Tài liệu tham khảo
G. N. Berestovskii, “A Property of Zeros of the Bessel Function J 0(μ),” Mat. Zametki 75, 302 (2004).
S. A. Beilin, “A Property of Zeros of the Bessel Function J v(x),” Vestn. Samar. Gos. Tekh. Univ., No. 30, 186–187 (2004).
A. N. Tikhonov and A. A. Samarskii, Equations of Mathematical Physics (Pergamon, Oxford, 1964; Nauka, Moscow, 1999).
Rayleigh (J. W. Strutt), “Note on the Numerical Calculation of the Roots of Fluctuating Functions,” Proc. London Math. Soc. 5, 112–194 (1874).
G. N. Watson, Treatise on the Theory of Bessel Functions (Inostrannaya Literatura, Moscow, 1949; Cambridge Univ. Press, Cambridge, 1952).
M. K. Kerimov, “The Rayleigh Function: Theory and Methods for Its Calculation,” Zh. Vychisl. Mat. Mat. Fiz. 39, 1962–2006 (1999) [Comput. Math. Math. Phys. 39, 1883–1925 (1999)].
M. G. Volynskaya, “On the Solvability of Nonlocal Problem with an Integral Condition,” Proceedings of II All-Russia Scientific Conference on Mathematical Modeling and Boundary Value Problems, Samara, June 1–3, 2005, part 3: Differential Equations and Boundary Value Problems (Samara, 2005), pp. 62–64.
M. K. Kerimov, “On the Calculation of the Rayleigh Function,” in Analytical and Numerical Methods for Problems in Mathematical Physics, Ed. by A. A. Abramov (Vychisl. Tsentr Akad. Nauk SSSR, Moscow, 1989) [in Russian].
P. L. Kapitsa, “Heat Conduction and Diffusion in a Liquid with Periodic Flow: I. Determination of the Wave Transport Coefficient in a Pipe, Slit, and Channel,” Zh. Eksp. Teor. Fiz. 21, 964–978 (1951).
P. L. Kapitsa, “Computation of Sums of Negative Even Powers of Zeros of Bessel Functions,” Dokl. Akad. Nauk SSSR 77, 561–564 (1951).
N. N. Meiman, “Recurrence Formulas for Power Sums of Zeros of Bessel Functions,” Dokl. Akad. Nauk SSSR 108, 190–193 (1956).