Zobrazeno 1 - 10
of 880
pro vyhledávání: '"harmonic numbers"'
Publikováno v:
Applied Mathematics in Science and Engineering, Vol 32, Iss 1 (2024)
Recently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.
Externí odkaz:
https://doaj.org/article/b3ba5276b2e04a5590687127f3157a1a
Autor:
Necdet Batır
Publikováno v:
Contributions to Mathematics, Vol 9, Pp 56-61 (2024)
Externí odkaz:
https://doaj.org/article/42b82d3431f04700a6c33a73d421c1b3
Autor:
Kwang-Wu Chen, Fu-Yao Yang
Publikováno v:
AIMS Mathematics, Vol 9, Iss 7, Pp 16885-16900 (2024)
Yamamoto's integral was the integral associated with 2-posets, which was first introduced by Yamamoto. In this paper, we obtained the values of infinite series involving harmonic numbers and reciprocal of binomial coefficients by using some technique
Externí odkaz:
https://doaj.org/article/e8869bb1faa841b5a5639d7a2d261618
Publikováno v:
Mathematical and Computer Modelling of Dynamical Systems, Vol 29, Iss 1, Pp 315-323 (2023)
ABSTRACTHarmonic numbers and generalized harmonic numbers have been studied in connection with combinatorial problems, many expressions involving special functions in analytic number theory and analysis of algorithms. We introduce Lerch-harmonic numb
Externí odkaz:
https://doaj.org/article/46846f5ca89645b1be4c025af5342c65
Publikováno v:
Mathematics, Vol 12, Iss 19, p 3000 (2024)
Relying on the Hurwitz formula, we find closed-form formulas for the series over sine and cosine functions through the Hurwitz zeta functions, and using them and another summation formula for trigonometric series, we obtain a finite sum for some seri
Externí odkaz:
https://doaj.org/article/24606386ac28484d8d4d32a129557850
Publikováno v:
Axioms, Vol 13, Iss 9, p 631 (2024)
We have derived alternative closed-form formulas for the trigonometric series over sine or cosine functions when the immediate replacement of the parameter appearing in the denominator with a positive integer gives rise to a singularity. By applying
Externí odkaz:
https://doaj.org/article/4fb7e4fb30a145c48de93e3872deb3d8
Autor:
Kwang-Wu Chen
Publikováno v:
Mathematics, Vol 12, Iss 17, p 2621 (2024)
In this paper, we express ∑n,m≥1ε1nε2mMn(u)Mm(v)nrms(n+m)t as a linear combination of alternating multiple zeta values, where εi∈{1,−1} and Mk(u)∈{Hk(u),H¯k(u)}, with Hk(u) and H¯k(u) being harmonic and alternating harmonic numbers, re
Externí odkaz:
https://doaj.org/article/e389618658954c26b6e59e78ecda48cc
Autor:
Chunli Li, Wenchang Chu
Publikováno v:
Mathematics, Vol 12, Iss 17, p 2685 (2024)
By employing the coefficient extraction method, a class of binomial series involving harmonic numbers will be reviewed through three hypergeometric F12(y2)-series. Numerous closed-form generating functions for infinite series containing binomial coef
Externí odkaz:
https://doaj.org/article/4e9cd5286a5a4947a95cbeeb3221876b
Autor:
Jizhen Yang, Yunpeng Wang
Publikováno v:
AIMS Mathematics, Vol 8, Iss 10, Pp 24331-24344 (2023)
In this paper, we establish some congruences mod $ p^3 $ involving the sums $ \sum_{k = 1}^{p-1}k^mB_{p, k}^{2l} $, where $ p > 3 $ is a prime number and $ B_{p, k} $ are generalized Catalan numbers. We also establish some congruences mod $ p^2 $ inv
Externí odkaz:
https://doaj.org/article/5fc548f23dbf48f29608267b44d8cb86
Publikováno v:
Demonstratio Mathematica, Vol 56, Iss 1, Pp 195-204 (2023)
The harmonic numbers and generalized harmonic numbers appear frequently in many diverse areas such as combinatorial problems, many expressions involving special functions in analytic number theory, and analysis of algorithms. The aim of this article
Externí odkaz:
https://doaj.org/article/bce23d73343d48029745a45efce8758f