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pro vyhledávání: '"Lima, F. M."'
Autor:
Lima, F. M. S.
As is well-known, the separation of variables in second order partial differential equations (PDEs) for physical problems with spherical symmetry usually leads to Cauchy's differential equation for the radial coordinate $r$ and Legendre's differentia
Externí odkaz:
http://arxiv.org/abs/2210.10942
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Autor:
Lima, F. M. S.
In a recent work, Farhi developed a Fourier series expansion for the function $\,\ln{\Gamma(x)}\,$ on the interval $(0,1)$, which allowed him to derive a nice formula for the constant $\,\eta := 2 \int_0^1{\ln{\Gamma(x)} \, \sin{(2 \pi x)} \, dx}$. A
Externí odkaz:
http://arxiv.org/abs/1906.04303
Autor:
Lima, F. M. S.
Publikováno v:
Journal of Analysis & Number Theory 5 (2), 91-96 (2017)
The arithmetic nature of values of some functions of a single variable, particularly, $\sin{z}$, $\cos{z}$, $\sinh{z}$, $\cosh{z}$, $e^z$, and $\ln{z}$, is a relevant topic in number theory. For instance, all those functions return transcendental val
Externí odkaz:
http://arxiv.org/abs/1310.7289
Autor:
Lima, F. M. S.
In this note, I develop step-by-step proofs of irrationality for $\,\zeta{(2)}\,$ and $\,\zeta{(3)}$. Though the proofs follow closely those based upon unit square integrals proposed originally by Beukers, I introduce some modifications which certain
Externí odkaz:
http://arxiv.org/abs/1308.2720
Autor:
Lima, F. M. S.
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 series surpasses those of all known similar series, including a classi
Externí odkaz:
http://arxiv.org/abs/1207.3139
Autor:
Lima, F. M. S.
In a recent work on Euler-type formulae for even Dirichlet beta values, i.e. $\beta{(2n)}$, I have derived an exact closed-form expression for a class of zeta series. From this result, I have conjectured closed-form summations for two families of zet
Externí odkaz:
http://arxiv.org/abs/1203.5660
Autor:
Lima, F. M. S.
Publikováno v:
Eur. J. Phys. 33, 101-113 (2012)
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 in literature, which may be attributed to our trust on Archimedes' la
Externí odkaz:
http://arxiv.org/abs/1110.5264
Autor:
Lima, F. M. S.
Publikováno v:
Turkish J. Analysis and Number Theory 6, 49 (2018)
In this note, starting with a little-known result of Kuo, I derive a recurrence relation for the Bernoulli numbers $B_{2 n}$, $n$ being any positive integer. This new recurrence seems advantageous in comparison to other known formulae since it allows
Externí odkaz:
http://arxiv.org/abs/1109.4694
Autor:
Lima, F. M. S.
Publikováno v:
Turkish Journal of Analysis & Number Theory 5 (4), 143-145 (2017)
In this shortnote, a series expansion technique introduced recently by Dancs and He for generating Euler-type formulae for odd zeta values $\:\zeta{(2 k +1)}$, $\zeta{(s)}$ being the Riemann zeta function and $k$ a positive integer, is modified in a
Externí odkaz:
http://arxiv.org/abs/1109.4605