Abstract
A method is given for the interpretation of a class of divergent integrals in terms of a sum of function evaluations over an arbitrary partition of the integration interval. The class of integrands considered includes functions continuous on the integration interval, except at a finite number of algebraic or algebraico-logarithmic singularities, and the delta function and related generalised functions, or products of these. The interpretation assigned to such integrals coincides with that of generalised function theory. Possible applications of the method to the computation of functions are discussed.
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References
Lighthill, M. J.: Introduction to Fourier analysis and generalised functions. Cambridge: University Press 1959.
Temple, G.: Proc. Roy. Soc. Lond. A228, 175 (1955).
Ninham, B. W., andJ. N. Lyness: Submitted to Numerische Mathematik (1965).
Navot, I.: (a) J. Math. and Phys.40, 271 (1961) ; (b) J. Math. and Phys.41, 155 (1962) ; (c) Math. Comp.17, 337 (1963)
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Ninham, B.W. Generalised functions and divergent integrals. Numer. Math. 8, 444–457 (1966). https://doi.org/10.1007/BF02166670
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DOI: https://doi.org/10.1007/BF02166670