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

 

Gauss quadrature rules for the evaluation of $ 2\pi^{-1/2} \int_0^\infty \exp(-x^2) f(x) dx$


Author: David Galant
Journal: Math. Comp. 23 (1969), 674-674
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Abstract | Additional Information

Abstract: Gauss quadrature rules for evaluating integrals of the form

$\displaystyle 2{\pi ^{ - 1/2}} - \smallint _0^\infty \exp ( - {x^2})f(x)dx$

have been calculated to $ {\text{20S}}$ for one to twenty nodes. The coefficients for the threeterm recurrence relation of the first twenty orthogonal polynomials associated with the weight function exp $ ( - {x^2})$ on the interval $ [0, \infty )$ are also tabulated to $ 20{\text{S}}$.


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-69-99859-7
PII: S 0025-5718(69)99859-7
Article copyright: © Copyright 1969 American Mathematical Society