Is Catalan’s Constant Rational?
نویسندگان
چکیده
This paper employs a contour integral method to derive and evaluate the infinite sum of Euler polynomial expressed in terms Hurwitz Zeta function. We provide formulae for several classes sums Riemann function fundamental mathematical constants, including Catalan’s constant. representation constant suggests it could be rational.
منابع مشابه
Lebesgue Constant Minimizing Bivariate Barycentric Rational Interpolation
The barycentric form is the most stable formula for a rational interpolant on a finite interval. The choice of the barycentric weights can ensure the absence of poles on the real line, so how to choose the optimal weights becomes a key question for bivariate barycentric rational interpolation. A new optimization algorithm is proposed for the best interpolation weights based on the Lebesgue cons...
متن کاملEventually constant solutions of a rational difference equation
We describe all the solutions of a rational difference equation from Putnam’s mathematical competition, which are eventually equal to its positive equilibrium x\over \tilda=1. As a consequence we give a new, elegant and short proof of the fact that the equation has a positive solution which is not eventually equal to one. Moreover, we show that almost all solutions of the equation are not event...
متن کاملWho Is (More) Rational?
Revealed preference theory offers a criterion for decision-making quality: if decisions are high quality then there exists a utility function that the choices maximize. We conduct a large-scale field experiment that enables us to test for consistency with utility maximization. We find that high-income and high-education subjects display greater levels of consistency than low-income and low-educ...
متن کاملBloch's Constant is Computable
We prove the computability of Bloch’s constant by presenting the first algorithm approximating the constant up to arbitrary precision.
متن کاملIs Syntactic Binding Rational?
Recent results show that both TAG and Minimalist grammars can be enriched with rational constraints without increasing their strong generative capacity, where a constraint is rational iff it can be computed by a bottom-up tree automaton. This raises the question which aspects of syntax can be adequately formalized using only such constraints. One of hardest phenomena commonly studied by syntact...
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: Mathematics
سال: 2022
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math10224251