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Approximations via Whittaker’s cardinal function. (English) Zbl 0332.41013


MSC:

41A30 Approximation by other special function classes
65D20 Computation of special functions and constants, construction of tables
65D15 Algorithms for approximation of functions
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References:

[1] Davis, P. J., Interpolation and Approximation (1963), Blaisdell: Blaisdell Waltham, Mass · Zbl 0111.06003
[2] Gabdulhaev, V. G., A general quadrature process and its application to the approximate solution of singular integral equations, Sov. Math. Dokl., 9, 386-389 (1968) · Zbl 0177.38901
[3] Goodrich, R. F.; Stenger, F., Movable singularities and quadrature, Math. Comp., 24, 283-299 (1970) · Zbl 0209.17803
[4] Goodwin, E. T., The evaluation of integrals of the form \(∝−∞^∞ à(x) e^{−x^2\) · Zbl 0033.07001
[5] Kresz, R., Interpolation auf einem unendlichen Intervall, Computing, 6, 274-288 (1970) · Zbl 0217.52201
[6] Martensen, E., Auf numerischen auswertung uneigentlicher Integrale, ZAMM, 48, T83-T85 (1968) · Zbl 0207.16202
[7] McNamee, J., Error bounds for the evaluation of integrals by the Euler-Maclaurin formula and by Gauss-type formulae, Math. Comp., 18, 368-381 (1964) · Zbl 0125.36202
[8] McNamee, J.; Stenger, F.; Whitney, E. L., Whittaker’s Cardinal Function in Retrospect, Math. Comp., 25, 141-154 (1971) · Zbl 0216.48502
[9] Moran, P. A.P., Approximate relation between series and integrals, Math. Comp., 12, 34-37 (1958) · Zbl 0084.11701
[10] Nörlund, N. E., Vorlesungen über Differenzenrechnung (1924), Springer: Springer Berlin · JFM 50.0315.02
[11] Schwartz, C., Numerical integration of analytic functions, Comput. Phys., 4, 191-201 (1967)
[12] Squire, W., Numerical evaluation of integrals using Moran transformation, West Virginia, Aerospace Engineering report No. TR-14 (1969)
[13] Stenger, F., The approximate solution of convolution-type integral equations, SIAM J. Math. Anal., 4, 536-555 (1973) · Zbl 0258.45005
[14] Stenger, F., Integration formulae based on the trapezoidal formula, J. Inst. Math. Appl., 12, 103-114 (1973) · Zbl 0262.65011
[15] Takahasi, H.; Mori, M., Quadrature formulas obtained by variable transformation, Numer. Math., 21, 206-219 (1973) · Zbl 0267.65016
[16] Timan, A. F., (Int. Ser. Monogr. Pure Appl. Math., Vol. 34 (1963), McMillan: McMillan New York), English transl. · Zbl 0125.03504
[17] Whittaker, E. T., On the functions which are represented by the expansions of the interpolation theory, (Proc. Roy. Soc. Edinburgh, 35 (1915)), 181-194 · JFM 45.0553.02
[18] Wittaker, J. M., On the cardinal function of interpolation theory, (Proc. Edinburgh Math. Soc. Ser. 1, 2 (1927)), 41-46 · JFM 53.0264.01
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