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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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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