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On modified divided differences. II

Author: Gertrude Blanch
Journal: Math. Comp. 8 (1954), 67-75
MSC: Primary 65.0X
MathSciNet review: 0061883
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  • [1] Arnold N. Lowan & Jack Laderman, ``On the distribution of errors in $ n$th tabular differences,'' Annals of Math. Statistics, v. 10, 1939, p. 360-364. One minor detail of the paper is faulty, but the results are correct. In evaluating integrals involving products of sines or cosines, it is stated, for example, that
    $\displaystyle \int_{ - \infty }^\infty {dt[\sin at]/{t^{2n + 1}} = [{{( - 1)}^n}{a^{2n}}/(2n)!]\int_0^\infty {dt\sin at/t.} } $
    This of course is not true, since the left-hand integral does not exist if $ n$ is different from zero. However, it turns out that the contribution from the region around the origin in a sum of such integrals vanishes, and the result is right. MR 0000759 (1:125h)
  • [2] A. van Wijngaarden, Afrondingsfouten MR3, Tevens ZW-(1950)-.001. Math. Centrum Rekenfdeling, Amsterdam (in Dutch). See also A. M. Ostrowski. Two Explicit Formulae for the Distribution Function of the sums of $ n$ Uniformly Distributed Independent Variables. Archiv d. Math., v. 3, 1952, p. 3-11.

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Article copyright: © Copyright 1954 American Mathematical Society

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