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The polynomial approximation to a function in a semi-infinite interval has been worked out by using a variant of Chebyshev polynomials. The same has been applied to solve the quadrature problem over the said interval.
[1] F. B. Hildebrand: Introduction to Numerical Analysis. McGraw-Hill, New York-London, 1956, p. 325-329. MR 0075670 | Zbl 0070.12401
[2] L. Fox, I. B. Parker: Chebyshev Polynomials in Numerical Analysis. Oxford University Press, 1968, pp. 68, 90. MR 0228149
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