Abstract
We propose a new method for the calculation of Bessel functions of the first kind of integral order. By using the Laplace transformation, we solve a linear differential equation that defines the generating function for the Bessel functions expressed in terms of continued fractions.
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References
K. G. Valeev, “On a method for the solution of systems of linear differential equations with sinusoidal coefficients,”Izv. Vyssh. Uchebn. Zaved., Ser. Radiofiz.,3, No. 6, 1113–1126 (1960).
A. N. Khovanskii,Application of Continued Fractions and Their Generalizations to Problems of Approximation Analysis [in Russian], Gostekhteoretizdat, Moscow (1956).
Y. Luke,Mathematical Functions and Their Approximations, Academic Press, New York (1975).
F. W. J. Olver,Asymptotics and Special Functions, Academic Press, New York-London (1974).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1704–1705, December, 1995.
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Valeev, K.G., Kostinskii, O.Y. Calculation of Bessel functions by using continued fractions. Ukr Math J 47, 1949–1950 (1995). https://doi.org/10.1007/BF01060968
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DOI: https://doi.org/10.1007/BF01060968