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Numerical quadrature and asymptotic expansions. (English) Zbl 0178.18402

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[1] M. J. Lighthill, Introduction to Fourier analysis and generalised functions, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, 1958. · Zbl 0078.11203
[2] E. T. Whittaker and G. N. Watson, A course of modern analysis, Cambridge Mathematical Library, Cambridge University Press, Cambridge, 1996. An introduction to the general theory of infinite processes and of analytic functions; with an account of the principal transcendental functions; Reprint of the fourth (1927) edition. · JFM 53.0180.04
[3] A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Higher Transcendental Functions, Vol. 1, (Calif. Inst. Tech. Bateman Manuscript Project), Chapter 1, McGraw-Hill, New York, 1953, MR 15, 419. · Zbl 0051.30303
[4] G. N. Watson, Theory of Bessel Functions, Cambridge Univ. Press, New York, 1958, p. 419.
[5] Israel Navot, An extension of the Euler-Maclaurin summation formula to functions with a branch singularity, J. Math. and Phys. 40 (1961), 271 – 276. · Zbl 0103.28804
[6] I. Navot, “A further extension of the Euler-Maclaurin summation formula,” J. Math, and Phys., v. 41, 1962, pp. 155-163. · Zbl 0109.28904
[7] Israel Navot, The Euler-Maclaurin functional for functions with a quasi-step discontinuity, Math. Comp. 17 (1963), 337 – 345. · Zbl 0117.11402
[8] P. C. Waterman, J. M. Yos, and R. J. Abodeely, Numerical integration of non-analytic functions, J. Math. and Phys. 43 (1964), 45 – 50. · Zbl 0221.65039
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