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Quadrature formulas for oscillatory integral transforms. (English) Zbl 0477.65090

65R10Integral transforms (numerical methods)
65D32Quadrature and cubature formulas (numerical methods)
65T40Trigonometric approximation and interpolation (numerical methods)
44A15Special transforms (Legendre, Hilbert, etc.)
42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
Full Text: DOI EuDML
[1] Abramowitz, A., Stegun, I.B.: Handbook of Mathematical Functions. NBS Appl. Math. Series 53, Washington DC 1964 · Zbl 0171.38503
[2] Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. New York: Academic Press 1975 · Zbl 0304.65016
[3] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher Transcendental Functions. Vol. 2, New York: McGraw-Hill 1953 · Zbl 0052.29502
[4] Gautschi, W.: Efficient computation of the complex error function. SIAM J. Numer. Anal.7, 187-198 (1970) · Zbl 0204.48304 · doi:10.1137/0707012
[5] Gautschi, W.: On Generating Orthogonal Polynomials. SIAM J. Scientific Statistical Comput. (to appear) · Zbl 0482.65011
[6] Hildebrand, F.B.: Introduction to Numerical Analysis. 2nd ed., New York: McGraw-Hill, 1974 · Zbl 0279.65001
[7] Krylov, V.I., Kruglikova, L.G.: A Handbook on Numerical Harmonic Analysis. (Russian). Izdat ?Nauka i Tehnika?, Minsk, 1968 [English translation by Israel Progr. Sci. Transl. Jerusalem 1969]
[8] Olver, F.W.J.: Asymptotics and Special Functions. New York: Academic Press, 1974 · Zbl 0303.41035
[9] Rabinowitz, P., Weiss, G.: Tables of abscissas and weights for numerical evaluation of integrals of the form $\int\limits_0^\infty {e^{ - x} x^n f(x)dx} $ , MTAC,13, 285-294 (1959) · Zbl 0094.11809
[10] Shao, T.S., Chen, T.C., Frank, R.M.: Tables of zeros and Gaussian weights of certain associated Laguerre polynomials and the related generalized Hermite polynomials. Math. Comput.18, 598-616 (1964) · Zbl 0123.34501 · doi:10.1090/S0025-5718-1964-0166397-1
[11] Stenger, F.: Numerical methods based on Whittaker cardinal, or sinc functions. SIAM Rev.23, 165-224 (1981) · Zbl 0461.65007 · doi:10.1137/1023037
[12] Stenger, F.: The asymptotic approximation of certain integrals. SIAM J. Math. Anal.1, 392-404 (1970) · Zbl 0203.37201 · doi:10.1137/0501036
[13] Szegö, G.: Orthogonal Polynomials. Colloquium Publication, Vol. 23, 4th ed., Amer. Math. Soc., Providence, R.I. 1975 · Zbl 0305.42011
[14] Ting, B.Y., Luke, Y.L.: Computation of integrals with oscillatory and singular integrands. Math. Comput.37, 169-183 (1981) · Zbl 0495.65008 · doi:10.1090/S0025-5718-1981-0616369-5
[15] Titchmarch, E.C.: The Theory of Functions. 2nd ed., Oxford, London, New York: University Press 1939
[16] Todd, J.: Evaluation of the exponential integral for large complex arguments. J. Res. Nat. Bur. Standards.52, 313-317 (1954) · Zbl 0055.36002
[17] Weber, H.: Numerical Computation of the Fourier Transform Using Laguerre Functions and the Fast Fourier Transform. Numer. Math.36, 197-209 (1981) · Zbl 0445.65114 · doi:10.1007/BF01396758
[18] Widder, D.V.: The Laplace Transform. Princeton: University Press, 1941 · Zbl 0063.08245
[19] Wong, R.: Error Bounds for asymptotic expansions of Hankel transforms. SIAM J. Math. Anal.7, 799-808 (1976) · Zbl 0339.44003 · doi:10.1137/0507061