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1 results

  • Asymptotic analysis and local lattice central limit theorems

  • P.A.P. Moran
  • Journal:
    Journal of Applied Probability / Volume 16 / Issue 3 / September 1979
    Published online by Cambridge University Press:
    14 July 2016, pp. 541-553
    Print publication:
    September 1979

  • Methods of evaluating the coefficients of high powers of functions defined by power series with positive coefficients are considered. Such methods, which were originally used by Laplace, can, for example, be used to obtain asymptotic formulae for Stirling numbers. They are equivalent to using local lattice central limit theorems. An alternative method using direct numerical integration on a contour integral giving the required coefficient is described. Exact bounds for the accuracy of this method can often be obtained by considerations of the unimodality of discrete distributions. The results are illustrated using convolutions of the rectangular and logarithmic distributions.