Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Vito Lampret"'
Autor:
Vito Lampret
Publikováno v:
Cubo, Vol 26, Iss 1, Pp 21-32 (2024)
Asymptotic estimates for the generalized Wallis ratio \(W^*(x):=\frac{1}{\sqrt{\pi}}\cdot\frac{\Gamma(x+\frac{1}{2})}{\Gamma(x+1)}\) are presented for \(x\in\mathbb{R}^+\) on the basis of Stirling's approximation formula for the \(\Gamma\) function.
Externí odkaz:
https://doaj.org/article/ba192fe89d364b13883a12f147de5487
Autor:
Vito Lampret
Publikováno v:
Cubo, Vol 23, Iss 3, Pp 357-368 (2021)
For any $a\in\R$, for every $n\in\N$, and for $n$-th Wallis' ratio $w_n:=\prod_{k=1}^n\frac{2k-1}{2k}$, the relative error $r_{\,\!_0}(a,n):=\big(v_{\,\!_0}(a,n)-w_n^a\big)/w_n^a$ of the approximation $w_n^a\approx v_{\,\!_0}(a,n):=(\pi n)^{-a/2} $ i
Externí odkaz:
https://doaj.org/article/a096a01c8c39422b983befa22f703fd8
Autor:
Vito Lampret
Publikováno v:
Cubo, Vol 21, Iss 2, Pp 51-64 (2019)
For the perimeter $P(a,b)$ of an ellipse with the semi-axes $a\ge b\ge 0$ a sequence $Q_n(a,b)$ is constructed such that the relative error of the approximation $ P(a,b)\approx Q_n(a,b)$ satisfies the following inequalities \begin{align*} 0\le -\
Externí odkaz:
https://doaj.org/article/c7976dfbdd2444f190ac9824447a33a3
Autor:
Vito Lampret
Publikováno v:
Bulletin of Mathematical Sciences, Vol 9, Iss 1, Pp 1950002-1-1950002-7 (2019)
For n ∈ ℕ the nth alternating harmonic number Hn∗ :=∑ k=1n(−1)k−1 1 k is given in the form Hn∗ =ln 2 + (−1)n+1 4⌊n+1 2 ⌋ +∑i=1q−1 (4i − 1)B 2i (2i)(2⌊n+1 2 ⌋)2i + rq(n), where q ∈ ℕ is a parameter controlling the
Externí odkaz:
https://doaj.org/article/7bd2c36615d44ae0b416bdf9a76a971a
Autor:
Vito Lampret
Publikováno v:
Mathematica Slovaca. 71:359-368
For the period T(α) of a simple pendulum with the length L and the amplitude (the initial elongation) α ∈ (0, π), a strictly increasing sequence Tn (α) is constructed such that the relations T 1 ( α ) = 2 L g π − 2 + 1 ϵ ln 1 + ϵ 1 − ϵ
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::82e6d40212f32ab5061fdc08c2bb71ba
https://doi.org/10.1515/ms-2017-0473
https://doi.org/10.1515/ms-2017-0473
Autor:
Vito Lampret
Publikováno v:
Mathematical Inequalities & Applications. :887-896
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a416b13a628b5ca610df0582d026493e
https://doi.org/10.7153/mia-2021-24-61
https://doi.org/10.7153/mia-2021-24-61
Autor:
Vito Lampret
Publikováno v:
Mediterranean Journal of Mathematics. 19
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::31a8c01a35d669840195f513cf732cd9
https://doi.org/10.1007/s00009-022-02000-x
https://doi.org/10.1007/s00009-022-02000-x
Autor:
Vito Lampret
Publikováno v:
Bulletin of the Malaysian Mathematical Sciences Society. 43:1343-1356
The 2-periodic function, $$W^*\in C^2({\mathbb {R}})$$ is constructed in such a way that the sum $$\sum _{k=1}^n(-1)^{k+1}f(k)$$ can be efficiently estimated for any $$n\in {\mathbb {N}}\cup \{\infty \} $$ and for every $$f\in C^4[1,\infty )$$ having
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16954b0b359a8bcc1ff5acc83162d4a9
https://doi.org/10.1007/s40840-019-00743-7
https://doi.org/10.1007/s40840-019-00743-7
Autor:
Vito Lampret
Publikováno v:
Mediterranean Journal of Mathematics. 18
For the perimeter P(a, b) of an ellipse with the semi-axes $$a\ge b>0$$ , a sequence $$P_n(a,b)$$ is constructed such that the relative error of the approximation $$ P(a,b)\approx P_n(a,b)$$ satisfies the following inequalities $$\begin{aligned} 0\le
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::3c0c153c73623c37d56357207ea7cef1
https://doi.org/10.1007/s00009-020-01650-z
https://doi.org/10.1007/s00009-020-01650-z
Autor:
Vito Lampret
Publikováno v:
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas. 115
Several new, accurate, asymptotic estimates for the ratio of two Gamma functions, $$Q_{\varGamma }(x,a,b):=\frac{\varGamma (x+a)}{\varGamma (x+b)}$$ , are obtained on the basis of Stirling’s approximation formula for the $$\varGamma $$ function.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::33ef70e8497c7c08d84c434fac428e11
https://doi.org/10.1007/s13398-020-00962-9
https://doi.org/10.1007/s13398-020-00962-9