منابع مشابه
Series of Error Terms for Rational Approximations of Irrational Numbers
Let pn/qn be the n-th convergent of a real irrational number α, and let εn = αqn−pn. In this paper we investigate various sums of the type ∑ m εm, ∑ m |εm|, and ∑ m εmx m. The main subject of the paper is bounds for these sums. In particular, we investigate the behaviour of such sums when α is a quadratic surd. The most significant properties of the error sums depend essentially on Fibonacci nu...
متن کاملA Toric Ring with Irrational Poincar E-betti Series
{ We show that there exists a toric curve in P 8 , whose homogeneous coordinate ring has a presentation with 12 quadratic relations and whose Poincar e-Betti series is irrational. The example was found by a computer search, aiming at a homological classiication of those toric curves that have a quadratic presentation in P n?1 for n 9. Some other consequences of this search are also presented. U...
متن کاملUniserial modules of generalized power series
Let R be a ring, M a right R-module and (S,≤) a strictly ordered monoid. In this paper we will show that if (S,≤) is a strictly ordered monoid satisfying the condition that 0 ≤ s for all s ∈ S, then the module [[MS,≤]] of generalized power series is a uniserial right [[RS,≤]] ]]-module if and only if M is a simple right R-module and S is a chain monoid.
متن کاملLogarithmic-Exponential Power Series
We use generalized power series to construct algebraically a nonstandard model of the theory of the real eld with exponentiation. This model enables us to show the undeenability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x)(log log x) is not asymptotic...
متن کاملOn Interpolating Power Series
We derive a simple error estimate for equally spaced, polynomial interpolation of power series that does not require the uniform bounds on derivatives of the Cauchy remainder. The key steps are expressing Newton coefficients in terms of Stirling numbers S(i, j) of the second kind and applying the concavity of lnS(i, j).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.2307/2033931