Zobrazeno 1 - 10
of 8 625
pro vyhledávání: '"Riemann zeta function"'
Autor:
Zhenjiang Pan, Zhengang Wu
Publikováno v:
AIMS Mathematics, Vol 9, Iss 6, Pp 16564-16585 (2024)
In this paper, we derive the asymptotic formulas $ B^*_{r, s, t}(n) $ such that $ \mathop{\lim} \limits_{n \rightarrow \infty} \left\{ \left( \sum\limits^{\infty}_{k = n} \frac{1}{k^r(k+t)^s} \right)^{-1} - B^*_{r,s,t}(n) \right\} = 0, $ where
Externí odkaz:
https://doaj.org/article/0c9acae53be64923a6ebcbe946741a8e
Autor:
Zhiling Fan, Wenchang Chu
Publikováno v:
Electronic Research Archive, Vol 32, Iss 2, Pp 1227-1238 (2024)
By making use of the multisection series method, four classes of alternating infinite series are evaluated, in closed form, by the Riemann zeta function and the Dirichlet beta function.
Externí odkaz:
https://doaj.org/article/3c5cf15a97ce4699ab3a7da64aaab3f4
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.
Autor:
Mohammad Abu-Ghuwaleh, Rania Saadeh
Publikováno v:
Arab Journal of Basic and Applied Sciences, Vol 30, Iss 1, Pp 675-690 (2023)
AbstractIn this paper, we introduce a ground-breaking approach to defining fractional calculus for a selected class of analytic functions. Our new definitions, based on a novel and intuitive understanding of fractional derivatives and integrals, offe
Externí odkaz:
https://doaj.org/article/29da911d6dbd4626a9b8b4443a79b578
Autor:
Zhenjiang Pan, Zhengang Wu
Publikováno v:
AIMS Mathematics, Vol 8, Iss 12, Pp 28558-28568 (2023)
In recent years, many mathematicians researched infinite reciprocal sums of various sequences and evaluated their value by the asymptotic formulas. We study the asymptotic formulas of the infinite reciprocal sums formed as $ \left(\sum^{\infty}_{k =
Externí odkaz:
https://doaj.org/article/6763eb6cb24a40f6a0de9c7d46f1e9a7
Autor:
Timothy Ganesan
Publikováno v:
Mathematics, Vol 12, Iss 17, p 2624 (2024)
Determining the exact number of primes at large magnitudes is computationally intensive, making approximation methods (e.g., the logarithmic integral, prime number theorem, Riemann zeta function, Chebyshev’s estimates, etc.) particularly valuable.
Externí odkaz:
https://doaj.org/article/0407b5e1d90444aca0336339f09fb2be
Autor:
Antanas Laurinčikas
Publikováno v:
Computation, Vol 12, Iss 8, p 164 (2024)
By the Bagchi theorem, the Riemann hypothesis (all non-trivial zeros lie on the critical line) is equivalent to the self-approximation of the function ζ(s) by shifts ζ(s+iτ). In this paper, it is determined that the Riemann hypothesis is equivalen
Externí odkaz:
https://doaj.org/article/e08de557d8bb4b5da59223420960a183
Autor:
Junesang Choi, Necdet Batır
Publikováno v:
Symmetry, Vol 16, Iss 7, p 932 (2024)
Numerous logarithmic integrals have been extensively documented in the literature. This paper presents an algorithmic evaluation of a specific class of these integrals. Our systematic approach, rooted in logarithmic principles, enables us to extend o
Externí odkaz:
https://doaj.org/article/da5a0a197b2045079f04b3b8152aef24
Akademický článek
Tento výsledek nelze pro nepřihlášené uživatele zobrazit.
K zobrazení výsledku je třeba se přihlásit.
K zobrazení výsledku je třeba se přihlásit.