Tables for the Gaussian computation of for values of varying continuously between and

Authors:
P. Lambin and J. P. Vigneron

Journal:
Math. Comp. **33** (1979), 805-811

MSC:
Primary 65A05

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521295-7

MathSciNet review:
521295

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Tables of coefficients of Chebyshev expansions for computing to 11 places the abscissas and weight factors of the 12-point generalized Gauss-Laguerre quadrature formula are presented.

**[1]**I. S. BEREZIN & N. P. ZHIDKOV,*Computing Methods*, Vol. I, Pergamon Press, Oxford, 1965, p. 236.**[2]**Z. KOPAL,*Numerical Analysis*, Wiley, New York, 1961.**[3]**Arthur Erdélyi, Wilhelm Magnus, Fritz Oberhettinger, and Francesco G. Tricomi,*Higher transcendental functions. Vols. I, II*, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953. Based, in part, on notes left by Harry Bateman. MR**0058756****[4]**Herbert E. Salzer and Ruth Zucker,*Table of the zeros and weight factors of the first fifteen Laguerre polynomials*, Bull. Amer. Math. Soc.**55**(1949), 1004–1012. MR**32191**, https://doi.org/10.1090/S0002-9904-1949-09327-8**[5]**D. BURNETT, "The numerical calculation of ,"*Proc. Cambridge Philos. Soc.*, v. 33, 1937, pp. 359-362.**[6]**Philip Rabinowitz and George Weiss,*Tables of abcissas and weights for numerical evaluation of integrals of the form ∫₀^{∞}𝑒^{-𝑥}𝑥ⁿ𝑓(𝑥)𝑑𝑥*, Math. Tables Aids Comput.**13**(1959), 285–294. MR**107992**, https://doi.org/10.1090/S0025-5718-1959-0107992-3**[7]**V. S. AIZENSHTAT, V. I. KRYLOV & A. S. METLESKII,*Tables for Calculating Laplace Transforms and Integrals of the Form*, Izdat. Akad. Nauk SSSR, Minsk, 1962 (Russian); reviewed in*Math. Comp.*, v. 17, 1963, p. 93.**[8]**P. Concus, D. Cassatt, G. Jaehnig, and E. Melby,*Tables for the evaluation of ∫₀^{∞}𝑥^{𝛽}𝑒^{-𝑥}𝑓(𝑥)𝑑𝑥 by Gauss-Laguerre quadrature*, Math. Comp.**17**(1963), 245–256. MR**158534**, https://doi.org/10.1090/S0025-5718-1963-0158534-9**[9]**P. CONCUS, "Additional tables for the evaluations of by Gauss-Laguerre quadrature,"*Math. Comp.*, v. 18, 1964, p. 523.**[10]**B. S. BERGER & R. DANSON, "Tables of zeros and weights for Gauss-Laguerre quadrature,"*Math. Comp.*, v. 22, 1968, pp. 458-459.**[11]**B. S. BERGER, R. DANSON & R. CARPENTER, "Tables of zeros and weights for Gauss-Laguerre quadrature to 24S for*N*= 400, 500 and 600, and tables of zeros and weights for Gauss-Laguerre quadrature to 23S for*N*= 700, 800 and 900,"*Math. Comp.*, v. 23, 1969, p. 882.**[12]**V. I. KRYLOV & P. P. VOROBLEVA, Izdat. Nauka i Teknika, Minsk, 1971.**[13]**E. N. DEKANOSIDZE,*Tables of the Zeros and Weight Factors of Generalized Laguerre Polynomials*, Computing Center, Acad. Sci. USSR, Moscow, 1966.**[14]**L. Fox and I. B. Parker,*Chebyshev polynomials in numerical analysis*, Oxford University Press, London-New York-Toronto, Ont., 1968. MR**0228149****[15]**Yudell L. Luke,*Mathematical functions and their approximations*, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. MR**0501762****[16]**J. H. Wilkinson,*The evaluation of the zeros of ill-conditioned polynomials. I, II*, Numer. Math.**1**(1959), 150–180. MR**109435**, https://doi.org/10.1007/BF01386381

Retrieve articles in *Mathematics of Computation*
with MSC:
65A05

Retrieve articles in all journals with MSC: 65A05

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0521295-7

Article copyright:
© Copyright 1979
American Mathematical Society