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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Evaluation of orthogonal polynomials and relationship to evaluating multiple integrals


Author: P. M. Hirsch
Journal: Math. Comp. 22 (1968), 280-285
MSC: Primary 65.55; Secondary 41.00
Corrigendum: Math. Comp. 22 (1968), 911.
MathSciNet review: 0226855
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  • [1] P. Appell, Sur une classe de polynômes à deux variables et le calcul approché des intégrales doubles, Ann. Fac. Sci. Toulouse Sci. Math. Sci. Phys. 4 (1890), no. 2, H1–H20 (French). MR 1508102
  • [2] A. Erdelyi et al., Higher Transcendental Functions, Vol. 2, Bateman Manuscript Project, McGraw-Hill, New York, 1953. MR 15, 419.
  • [3] Philip J. Davis, Interpolation and approximation, Blaisdell Publishing Co. Ginn and Co. New York-Toronto-London, 1963. MR 0157156 (28 #393)
  • [4] Wolfgang Gröbner, "Über die Konstruktion von Systemen orthogonaler Polynome in ein- und zwei-dimensionalen Bereichen," Monatsh. Math., v. 52, 1948, pp. 38-54. MR 9, 430.
  • [5] Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869 (11,504d)
  • [6] Preston C. Hammer, Numerical evaluation of multiple integrals, On numerical approximation. Proceedings of a Symposium, Madison, April 21-23, 1958, Edited by R. E. Langer. Publication no. 1 of the Mathematics Research Center, U.S. Army, the University of Wisconsin, The University of Wisconsin Press, Madison, 1959, pp. 99–115. MR 0100355 (20 #6788)
  • [7] F. B. Hildebrand, Introduction to numerical analysis, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1956. MR 0075670 (17,788d)
  • [8] P. M. Hirsch, Numerical Evaluation and Estimation of Multiple Integrals, Ph.D. Thesis, Univ. of Wisconsin, Madison, Wis., 1966. (Unpublished.)
  • [9] Johann Radon, Zur mechanischen Kubatur, Monatsh. Math. 52 (1948), 286–300 (German). MR 0033206 (11,405b)
  • [10] A. H. Stroud, Integration formulas and orthogonal polynomials, SIAM J. Numer. Anal. 4 (1967), 381–389. MR 0228180 (37 #3764)
  • [11] Vladimir Tchakaloff, Formules de cubatures mécaniques à coefficients non négatifs, Bull. Sci. Math. (2) 81 (1957), 123–134 (French). MR 0094632 (20 #1145)
  • [12] Morris Weisfeld, Orthogonal polynomials in several variables, Numer. Math. 1 (1959), 38–40. MR 0102902 (21 #1687)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1968-0226855-1
PII: S 0025-5718(1968)0226855-1
Article copyright: © Copyright 1968 American Mathematical Society