79 citations · 125 across the 14 of their papers we have counts for
16 papers
Closed-form expressions for Farhi's constant and related integrals and its generalization
F. M. S. Lima
In a recent work, Farhi developed a Fourier series expansion for the function on the interval , which allowed him to derive a nice formula for the constant $…
Some transcendence results from a harmless irrationality theorem
F. M. S. Lima
The arithmetic nature of values of some functions of a single variable, particularly, , , , , , and , is a relevant topic in numb…
Beukers-like proofs of irrationality for and
F. M. S. Lima
In this note, I develop step-by-step proofs of irrationality for and . Though the proofs follow closely those based upon unit-square integrals proposed origi…
A rapidly converging Ramanujan-type series for Catalan's constant
F. M. S. Lima
In this note, by making use of a known hypergeometric series identity, I prove two Ramanujan-type series for the Catalan's constant. The convergence rate of these central binomial…
A simpler proof of a Katsurada's theorem and rapidly converging series for and
F. M. S. Lima
In a recent work on Euler-type formulae for even Dirichlet beta values, i.e. , I have derived an exact closed-form expression for a class of zeta series. From this result,…
Using surface integrals for checking the Archimedes' law of buoyancy
F. M. S. Lima
A mathematical derivation of the force exerted by an \emph{inhomogeneous} (i.e., compressible) fluid on the surface of an \emph{arbitrarily-shaped} body immersed in it is not found…
A shortened recurrence relation for the Bernoulli numbers
F. M. S. Lima
In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers , being any positive integer. This new recurrence se…
Another elementary proof of and a recurrence formula for
F. M. S. Lima
In this shortnote, a series expansion technique introduced recently by Dancs and He for generating Euler-type formulae for odd zeta values , being the Riema…
Some transcendental functions with an empty exceptional set
D. Marques, F. M. S. Lima
A transcendental function usually returns transcendental values at algebraic points. The (algebraic) exceptions form the so-called \emph{exceptional set}, as for instance the unita…
New definite integrals and a two-term dilogarithm identity
F. M. S. Lima
Among the several proofs known for , the one by Beukers, Calabi, and Kolk involves the evaluation of $\,\int_0^1 {\int_0^1{1/(1-x^2 y^2) \, dx}…
Counterexamples to the conjectured transcendence of , 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 is a transcendental number for all integer , , and $\,α\in \mathbb{Q…
An Euler-type formula for 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 , being a positive integer, which contains a series they could not reduce to a finite closed-f…
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…
A shortcut for evaluating some log integrals from products and limits
F. M. S. Lima
In this short paper, I introduce an elementary method for exactly evaluating the definite integrals , , $\int_0^{π/2}…
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 , being a rational number between and ,…
An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime
F M S Lima, P Arun
A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of l…