منابع مشابه
Euler-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 کاملNotes 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 کاملHypergeometric summation revisited
We consider hypergeometric sequences i e the sequences which satisfy linear rst order homogeneous recurrence equations with rela tively prime polynomial coe cients Some results related to necessary and su cient conditions are discussed for validity of discrete Newton Leibniz formula P w k v t k u w u v when u k R k t k and R k is a rational solution of Gosper s equation
متن کاملEuler–Maclaurin summation and Schlömilch series
A method for analysing a class of divergent series is developed from the Euler– Maclaurin summation formula. The conditions that the summand must satisfy are explored, and a significant simplification is obtained for cases where the summation ranges over all integers. As an example, we consider the Ewald representation for Schlömilch series, and show that this includes Twersky’s dual series for...
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2009
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2009.11920954