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

MSC:
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
References:
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[2]Davis, P.J., Rabinowitz, P.: Methods of Numerical Integration. New York: Academic Press 1975
[3]Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher Transcendental Functions. Vol. 2, New York: McGraw-Hill 1953
[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)
[6]Hildebrand, F.B.: Introduction to Numerical Analysis. 2nd ed., New York: McGraw-Hill, 1974
[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
[9]Rabinowitz, P., Weiss, G.: Tables of abscissas and weights for numerical evaluation of integrals of the form 0 e -x x n f(x)dx , MTAC,13, 285-294 (1959)
[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) · 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
[14]Ting, B.Y., Luke, Y.L.: Computation of integrals with oscillatory and singular integrands. Math. Comput.37, 169-183 (1981) · 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)
[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
[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