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pro vyhledávání: '"40C99"'
Autor:
Vignat, C., Milgram, M.
Publikováno v:
Journal of Integer Sequences, Vol. 27 (2024),Article 24.5.5
This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product or summation identities involving special functions including Gamma,
Externí odkaz:
http://arxiv.org/abs/2305.17585
Autor:
Dawson, Robert J. MacG., Molnar, Grant
In this paper, extending our earlier program, we derive maximal canonical extensions for multiplicative summations into algebraically closed fields. We show that there is a well-defined analogue to minimal polynomials for a series algebraic over a ri
Externí odkaz:
http://arxiv.org/abs/2111.09938
Autor:
Astar, W.
A derivation of the Z-transform of the Levi-Civita symbol is carried out up to 3 dimensions, and generalized to higher dimensions. Using its Z-transforms, corresponding expressions for the Laplace transform are also found, using Tustin's transform
Externí odkaz:
http://arxiv.org/abs/2110.03056
Autor:
Dawson, Robert, Molnar, Grant
A summation is a shift-invariant ${\rm R}$-module homomorphism from a submodule of ${\rm R}[[\sigma]]$ to ${\rm R}$ or another ring. [11] formalized a method for extending a summation to a larger domain by telescoping. In this paper, we revisit teles
Externí odkaz:
http://arxiv.org/abs/2105.04592
Autor:
Azevedo, Douglas, Andrade, Thiago P.
Publikováno v:
Communications in Mathematics, Volume 30 (2022), Issue 1 (May 12, 2022) cm:9290
In this paper, we propose extensions for the classical Kummer test, which is a very far-reaching criterion that provides sufficient and necessary conditions for convergence and divergence of series of positive terms. Furthermore, we present and discu
Externí odkaz:
http://arxiv.org/abs/2101.03402
Publikováno v:
Communications of the Blyth Institute 2:1 (2019) 7-15
Treating divergent series properly has been an ongoing issue in mathematics. However, many of the problems in divergent series stem from the fact that divergent series were discovered prior to having a number system which could handle them. The infin
Externí odkaz:
http://arxiv.org/abs/1804.11342
Autor:
Milgram, Michael
Publikováno v:
Journal of Classical Analysis, Volume 13, Number 1, January 2018
The question was asked: Is it possible to express the function \begin{equation} \tag{1.1} h(a)\equiv\,{_4F_3}(a,a,a,a;2a,a+1,a+1;1) \label{question} \end{equation} in closed form? After considerable analysis, the answer appears to be "no", but during
Externí odkaz:
http://arxiv.org/abs/1803.03135
Publikováno v:
2017 J. Phys. Commun. 1 025005
We present a method to sum Borel- and Gevrey-summable asymptotic series by matching the series to be summed with a linear combination of asymptotic series of known functions that themselves are scaled versions of a single, appropriate, but otherwise
Externí odkaz:
http://arxiv.org/abs/1706.00329
Autor:
Maity, Manojit
Publikováno v:
East-West Journal of Mathematics 2016, 87 (2016) 113305
In this paper, we introduce the notions of pointwise rough statistical convergence and rough statistically Cauchy sequences of real valued functions in the line of A. (T$\ddot{u}$rkmenoglu) G$\ddot{o}$khan and M. G$\ddot{u}$ng$\ddot{o}$r \cite{Tu1}.
Externí odkaz:
http://arxiv.org/abs/1603.00180
Autor:
Hardtke, Jan-David
Recently P. Das, S. Dutta and E. Savas introduced and studied the notions of strong $A^I$-summability with respect to an Orlicz function $F$ and $A^I$-statistical convergence, where $A$ is a non-negative regular matrix and $I$ is an ideal on the set
Externí odkaz:
http://arxiv.org/abs/1210.1350