Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Application of ultraspherical polynomials to non-linear oscillations. II. Free oscillations

Authors: Harry H. Denman and Y. King Liu
Journal: Quart. Appl. Math. 22 (1965), 273-292
MSC: Primary 65.60
DOI: https://doi.org/10.1090/qam/199965
MathSciNet review: 199965
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  • [1] H. H. Denman and J. E. Howard, Application of ultraspherical polynomials to non-linear oscillations. I. Free oscillation of the pendulum, Q. Appl. Math. 21 (1964) 325 MR 0155052
  • [2] Tables of the Chebyshev polynomials, National Bureau of Standards, Applied Mathematics Series 9 (U. S. Government Printing Office, 1952), Introduction
  • [3] N. W. McLachlan, Ordinary non-linear differential equations, 2nd Edition, Oxford University Press, London, 1956, p. 24-31, p. 39-40 MR 0093612
  • [4] B. O. Pierce and R. M. Foster, A short table of integrals, 4th Edition, Ginn and Co., Boston, 1956, p. 99-102
  • [5] P. F. Byrd and M. D. Friedmann, Handbook of elliptic integrals for engineers and physicists, Springer, Berlin, 1954, p. 50 MR 0060642
  • [6] E. Jahnke, F. Emde and F. Lösch, Tables of higher functions, 6th Edition, McGraw-Hill, New York, 1960
  • [7] P. Franklin, Methods of advanced calculus, McGraw-Hill, New York, 1944, p. 392 MR 0010896
  • [8] G. N. Watson, Theory of Bessel functions, 2nd Edition, Cambridge University Press, 1958, p. 369, eq. (8)
  • [9] H. H. Denman, Computer generation of optimized subroutines, Jour. Assoc. Comp. Mach. 8 (1961) 1
  • [10] N. Kryloff and N. Bogoliuboff, Introduction to non-linear mechanics, Princeton University Press, Princeton, 1943; N. Bogoliuboff and A. Mitropolsky, Asymptotic methods in the theory of non-linear oscillations, 2nd Edition, Gordon and Breach, New York, 1961 MR 0007461

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DOI: https://doi.org/10.1090/qam/199965
Article copyright: © Copyright 1965 American Mathematical Society

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