منابع مشابه
Notes on Euler-boole Summation
We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases in a general approach to approximation that also encompasses Taylor sums. Here we give additional details of the construction.
متن کاملEuler-boole Summation Revisited
is a well-known formula from classical analysis giving a relation between the finite sum of values of a function f , whose first m derivatives are absolutely integrable on [a, n], and its integral, for a,m, n ∈ N, a < n. This elementary formula appears often in introductory texts [2, 17], usually in reference to a particular application—Stirling’s asymptotic formula. However, general approaches...
متن کاملEuler-Boole Summation Revisited
We study a connection between Euler-MacLaurin Summation and Boole Summation suggested in an AMM note from 1960, which explains them as two cases of a general approach to approximation. Herein we give details and extensions of this idea.
متن کاملA Note on Lerch’s Formulae for Euler Quotients
Lerch’s formulae for Euler quotients in the rings Z and Fq[t] have already been studied. In this paper, we extend the study of these quotients to number fields and the Carlitz module. In the number fields case, we prove a version of Lerch’s formula for OKHil , the ring of integers of the Hilbert class field of a number field K. In the Fq[t] case, we replace the usual multiplication in Fq[t] wit...
متن کاملUnusual Formulae for the Euler Characteristic
Everyone knows that the Euler characteristic of a combinatorial manifold is given by the alternating sum of its numbers of simplices. It is shown that there are other linear combinations of the numbers of simplices which are combinatorial invariants, but that all such invariants are multiples of the Euler characteristic. Theorem [Pachner 1987, [3]]. Two closed combinatorial n-manifolds are PLho...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2004
ISSN: 1331-4343
DOI: 10.7153/mia-07-05