Numerical quadrature rules for some infinite range integrals
Author:
Avram Sidi
Journal:
Math. Comp. 38 (1982), 127142
MSC:
Primary 65D32
MathSciNet review:
637291
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Abstract: Recently the present author has given a new approach to numerical quadrature and derived new numerical quadrature formulas for finite range integrals with algebraic and/or logarithmic endpoint singularities. In the present work this approach is used to derive new numerical quadrature formulas for integrals of the form and , where is the exponential integral. It turns out the new rules are of interpolatory type, their abscissas are distinct and lie in the interval of integration and their weights, at least numerically, are positive. For fixed the new integration rules have the same set of abscissas for all p. Finally, the new rules seem to be at least as efficient as the corresponding Gaussian quadrature formulas. As an extension of the above, numerical quadrature formulas for integrals of the form too are considered.
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 S. Chandrasekhar, The Transfer of Radiant Energy, Clarendon Press, Oxford, 1953.
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 A. Sidi, ``Convergence properties of some nonlinear sequence transformations,'' Math. Comp., v. 33, 1979, pp. 315326. MR 514827 (81h:65003)
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 A. Sidi, ``Numerical quadrature and nonlinear sequence transformations; unified rules for efficient computation of integrals with algebraic and logarithmic endpoint singularities,'' Math. Comp., v. 34, 1980, pp. 851874. MR 572861 (81h:65017)
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 A. Sidi, ``Analysis of convergence of the Ttransformation for power series,'' Math. Comp., v. 34, 1980, pp. 833850. MR 572860 (83d:41039)
 [10]
 A. Sidi, Converging Factors for Some Asymptotic Moment Series That Arise in Numerical Quadrature, TR # 165, Computer Science Dept., Technion, Haifa.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198206372915
PII:
S 00255718(1982)06372915
Article copyright:
© Copyright 1982 American Mathematical Society
