On the accurate computation of the prolate spheroidal radial functions of the second kind
Authors:
T. Do-Nhat and R. H. MacPhie
Journal:
Quart. Appl. Math. 54 (1996), 677-685
MSC:
Primary 33C05; Secondary 33C45, 65D20
DOI:
https://doi.org/10.1090/qam/1417231
MathSciNet review:
MR1417231
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Abstract: The series expansion of the prolate radial functions of the second kind, expressed in terms of the spherical Neumann functions, converges very slowly when the spheroid’s surface coordinate $\xi$ approaches 1 (thin spheroids). In this paper an analytical series expansion in powers of $\left ( {{\xi ^2} - 1} \right )$ is obtained to facilitate the convergence. Then, by using the Wronskian test, it is shown that this newly developed expansion has been computed with a double precision accuracy.
J. A. Stratton, P. M. Morse, L. J. Chu, D. C. Little, and F. J. Carbato, Spheroidal Wave Functions, John Wiley and Sons, New York, 1956
C. Flammer, Spheroidal Wave Functions, Stanford Univ. Press, Stanford, Calif., 1957
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, 1953
B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16, 2378–2381 (1975)
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge Univ. Press, New York, 1980
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1970
J. A. Stratton, P. M. Morse, L. J. Chu, D. C. Little, and F. J. Carbato, Spheroidal Wave Functions, John Wiley and Sons, New York, 1956
C. Flammer, Spheroidal Wave Functions, Stanford Univ. Press, Stanford, Calif., 1957
P. M. Morse and H. Feshbach, Methods of Theoretical Physics, McGraw-Hill, New York, 1953
B. P. Sinha and R. H. MacPhie, On the computation of the prolate spheroidal radial functions of the second kind, J. Math. Phys. 16, 2378–2381 (1975)
E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge Univ. Press, New York, 1980
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1970
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Article copyright:
© Copyright 1996
American Mathematical Society