Series like Taylor's series
A theorem and some examples are given concerning the convergence, in a space of generalized functions, of power series whose terms contain successive derivatives of a given function. One example is the Euler-Maclaurin sum formula, where there are some novelties.
AMS (1980) subject classificationPrimary 40A30, 44A30 Secondary 65B15, 30D05, 44A10, 44A35
Unable to display preview. Download preview PDF.
- Erdelyi, A., Magnus, W., Oberhettinger, F., andTricomi, F. G.,Tables of integral transforms, Vol. 1. Bateman Manuscript Project, McGraw Hill, New York, 1954.Google Scholar
- Hardy, G. H.,Divergent series. Oxford University Press, 1963.Google Scholar
- Miller, J. B.,Generalized-function calculi for the Laplace transformation. Arch. Rational Mech. Anal.12 (1963), 409–419.Google Scholar
- Miller, J. B.,The Euler-Maclaurin sum formula for an inner derivation. Aequationes Math.25 (1982), 42–51.Google Scholar
- Miller, J. B.,The Euler-Maclaurin sum formula for a closed derivation. J. Austral. Math. Soc., Series A, to appear.Google Scholar
- Miller, J. B.,The Euler-Maclaurin formula generated by a summation operator. Proc. Royal Soc. Edinburgh, to appear.Google Scholar
- Titchmarsh, E. C.,Introduction to the theory of Fourier integrals. Oxford, Clarendon, 1950.Google Scholar
- Whittaker, E. T. andWatson, G. N.,A course of modern analysis. Cambridge University Press, Cambridge, 1946.Google Scholar