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