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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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The $\nu$-zeros of $J_{-\nu }(x)$
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by S. Conde and S. L. Kalla PDF
Math. Comp. 33 (1979), 423-426 Request permission

Abstract:

We compute the positive $\nu$-zeros of ${J_{ - \nu }}(x)$, regarded as a function of $\nu$. ${J_\nu }(x)$ stands for the Bessel function of first kind of order $\nu$. Some related inequalities are verified and algorithms the computer uses are described briefly.
References
    S. CONDE & S. L. KALLA, Tabla de Funciones de Bessel y Raíces de Ecuaciones Transcendentes Relacionadas, Facultad de Ingeniería, Universidad del Zulia, 1977. I. S. GRADSTEHYN & I. M. RYZHIK, Tables of Integrals, Series and Products, 4th ed., Academic Press, New York, 1965.
  • N. N. Lebedev, Special functions and their applications, Revised English edition, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965. Translated and edited by Richard A. Silverman. MR 0174795, DOI 10.1063/1.3047047
  • Yudell L. Luke, Mathematical functions and their approximations, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR 0501762
  • D. Naylor, On an integral transform occurring in the theory of diffraction, SIAM J. Math. Anal. 8 (1977), no. 3, 402–411. MR 438051, DOI 10.1137/0508030
  • G. N. Watson, A treatise on the theory of Bessel functions, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1995. Reprint of the second (1944) edition. MR 1349110
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Math. Comp. 33 (1979), 423-426
  • MSC: Primary 65D20
  • DOI: https://doi.org/10.1090/S0025-5718-1979-0514838-0
  • MathSciNet review: 514838