Topic
Indefinite sum
About: Indefinite sum is a research topic. Over the lifetime, 232 publications have been published within this topic receiving 3679 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, the properties of a certain operative symbol which appears to be of great utility in discussing q-functions are investigated, and the first part of the paper will consist of an investigation into the various forms ofand the nature of the inverse operations symbolised by Δ−n.
Abstract: In this paper my object is, primarily, to investigate the properties of a certain operative symbol which appears to be of great utility in discussing q-functions. The first part of the paper will consist of an investigation into the various forms ofand the nature of the inverse operations symbolised by Δ−n. With certain restrictions as to continuity, etc., φ(x) will denote an arbitrary function of x.
848 citations
PARC1
TL;DR: In this paper, a sum-mand an is given and the goal is to find those S(n) with the property [Formula: see text] with respect to a given an.
Abstract: Given a summand an, we seek the “indefinite sum” S(n) determined (within an additive constant) by [Formula: see text] or, equivalently, by [Formula: see text] An algorithm is exhibited which, given an, finds those S(n) with the property [Formula: see text] With this algorithm, we can determine, for example, the three identities [Formula: see text] [Formula: see text] and [Formula: see text] and we can also conclude that [Formula: see text] is inexpressible as S(m) - S(0), for any S(n) satisfying Eq. 2.
414 citations
TL;DR: In this article, the stability area for the difference system with the Caputo forward difference operator is described. But the stability conditions are not explicit and involve the decay rate of the solutions.
Abstract: Abstract The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples.
189 citations
TL;DR: In this article, the authors define the kind of person that will need some linear operators in spaces with an indefinite metric reference, i.e., people with open minded will always try to seek for the new things and information from many sources.
Abstract: Well, someone can decide by themselves what they want to do and need to do but sometimes, that kind of person will need some linear operators in spaces with an indefinite metric references. People with open minded will always try to seek for the new things and information from many sources. On the contrary, people with closed mind will always think that they can do it by their principals. So, what kind of person are you?
131 citations
TL;DR: The fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c is determined, and a Mercerian theorem is derived.
Abstract: We determine the fine spectrum of the generalized difference operator B(r,s) defined by a band matrix over the sequence spaces c0 and c, and derive a Mercerian theorem. This generalizes our earlier work (2004) for the difference operator Δ, and includes as other special cases the right shift and the Zweier matrices.
106 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2019 | 2 |
| 2018 | 3 |
| 2017 | 10 |
| 2016 | 8 |
| 2015 | 15 |
| 2014 | 12 |