F. Lima

activity

20052019

most citedAn accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

79 citations · 125 across the 14 of their papers we have counts for

collaborators

Showing 2009 · math.NTShow all

4 papers · 2 filters

math.NT2009

Counterexamples to the conjectured transcendence of $\sum 1/ (n + α)^{k}$ , its closed-form summation and extensions to polygamma functions and zeta series

F. M. S. Lima

In a recent work, Gun and co-workers have proposed that $\sum_{n = - \infty}^{\infty} (n + α)^{- k}$ is a transcendental number for all integer $k$ , $k > 1$ , and $\,α\in \mathbb{Q…

math.NT2009★ 11 cited

An Euler-type formula for $β (2 n)$ and closed-form expressions for a class of zeta series

F. M. S. Lima

In a recent work, Dancs and He found an Euler-type formula for $ζ (2 n + 1)$ , $n$ being a positive integer, which contains a series they could not reduce to a finite closed-f…

math.NT2009

Approximate expressions for mathematical constants from PSLQ algorithm: a simple approach and a case study

F. M. S. Lima

In this note, I present a simple PSLQ code for finding null linear combinations, with the best rational coefficients, of mathematical constants, within some prescribed precision. A…

math.NT2009

On the possible exceptions for the transcendence of the log-gamma function at rational entries

F. M. S. Lima

In a recent work [JNT \textbf{129}, 2154 (2009)], Gun and co-workers have claimed that the number $lo g Γ (x) + lo g Γ (1 - x)$ , $x$ being a rational number between $0$ and $1$ ,…

Counterexamples to the conjectured transcendence of ∑1/(n+α)k, its closed-form summation and extensions to polygamma functions and zeta series

An Euler-type formula for β(2n) and closed-form expressions for a class of zeta series

Approximate expressions for mathematical constants from PSLQ algorithm: a simple approach and a case study

On the possible exceptions for the transcendence of the log-gamma function at rational entries

Counterexamples to the conjectured transcendence of $\sum 1/ (n + α)^{k}$ , its closed-form summation and extensions to polygamma functions and zeta series

An Euler-type formula for $β (2 n)$ and closed-form expressions for a class of zeta series