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

 

Quadrature formulas for semi-infinite integrals


Authors: Ravindra Kumar and M. K. Jain
Journal: Math. Comp. 28 (1974), 499-503
MSC: Primary 65D30
Erratum: Math. Comp. 56 (1991), 407.
MathSciNet review: 0343549
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Abstract | References | Similar Articles | Additional Information

Abstract: Polynomials orthogonal on $ [0,\infty ]$ with regard to the weight function $ w(x) = {x^\alpha }{(1 + x)^{ - \beta }}$ are obtained, recurrence relations are found and the differential equation, which is satisfied by them, is given. Formulas for weights and abscissas in the corresponding quadrature formula are given.


References [Enhancements On Off] (What's this?)

  • [1] W. M. Harper, "Quadrature formulas for infinite integrals," Math. Comp., v. 16, 1962, pp. 170-175. MR 26 #3185. MR 0145656 (26:3185)
  • [2] F. B. Hildebrand, Introduction to Numerical Analysis, McGraw-Hill, New York, 1956, pp. 258-367. MR 17, 788. MR 0075670 (17:788d)
  • [3] A. H. Stroud & Don Secrest, Gaussian Quadrature Formulas, Prentice-Hall, Englewood Cliffs, N.J., 1966, p. 254. MR 34 #2185. MR 0202312 (34:2185)
  • [4] G. Szegö, Orthogonal Polynomials, 2nd rev. ed., Amer. Math. Soc. Colloq. Publ., vol. 23, Amer. Math. Soc., Providence, R.I., 1959, pp. 58-72. MR 21 #5029. MR 0106295 (21:5029)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1974-0343549-5
PII: S 0025-5718(1974)0343549-5
Keywords: Orthogonal polynomials, weight function, recurrence relation, quadrature formula, weight coefficients, error
Article copyright: © Copyright 1974 American Mathematical Society