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