Binomial convolution and transformations of Appell polynomials

Adell, José A.; Lekuona, Alberto

doi:10.1016/j.jmaa.2017.06.077

Cited by 16 publications

(18 citation statements)

References 34 publications

(39 reference statements)

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“…Likewise, (1) shows that Q(e xB (t ) )(x, t ) = ∞ n=1b n n! B (t ) n e xB (t ) = B (B (t ))e xB (t ) = t e xB (t ) , equality that proves the last equation in (3).…”

Section: Preliminaries On Sheffer Sequencesmentioning

confidence: 55%

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Appell and Sheffer sequences: on their characterizations through functionals and examples

Carrillo¹,

Hurtado²

2021

Comptes Rendus. Mathématique

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The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equivalent to several well-known characterizations appearing in the literature. We also give several examples, including integral representations of the inverse operators associated to Bernoulli and Euler polynomials, and a new integral representation of the re-scaled Hermite d-orthogonal polynomials generalizing the Weierstrass operator related to the Hermite polynomials. Résumé. L'objectif de cet article est de présenter une nouvelle récurrence simple pour les suites d'Appell et de Sheffer en termes de la fonctionnelle linéaire qui les définit, et d'expliquer comment cela équivaut à plusieurs caractérisations bien connues qui apparaissent dans la littérature. Nous donnons aussi plusieurs exemples, y compris des représentations intégrales des opérateurs inverses associés aux polynômes de Bernoulli et d'Euler, et une nouvelle représentation intégrale des polynômes d'Hermite d-orthogonaux remis à l'échelle, qui généralise l'opérateur de Weierstrass associé aux polynômes d'Hermite.

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“…Likewise, (1) shows that Q(e xB (t ) )(x, t ) = ∞ n=1b n n! B (t ) n e xB (t ) = B (B (t ))e xB (t ) = t e xB (t ) , equality that proves the last equation in (3).…”

Section: Preliminaries On Sheffer Sequencesmentioning

confidence: 55%

“…In contrast, a more recent approach has been made using matrix and determinantal representations, see, e.g., [1,2,13,14,37,38]. Also, current research has focussed on special sequences [16] and other alternative descriptions of the theory, for instance, through random variables [3,33].…”

Section: Introductionmentioning

confidence: 99%

Appell and Sheffer sequences: on their characterizations through functionals and examples

Carrillo¹,

Hurtado²

2021

Comptes Rendus. Mathématique

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“…Differentiating this expression with respect to to θ and taking into account (12) and (19), we obtain (16). Choosing y 1 = • • • = y k = 1 in (16) and recalling (13) and 15, we get (17).…”

Section: Technical Resultsmentioning

confidence: 99%

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

Adell

Lekuona

2019

Adv Differ Equ

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“…Based on the latitude and longitude of a task, with each independent task as the center, and the dimensions being extended 0.2 units in the surrounding (southeast northwest) directions, the area that each task contains is called the field. The field is a sociological concept [37], specifically referring to the relationships within the independent space. This paper distinguishes the concept from the grid.…”

Section: B Index Selectionmentioning

confidence: 99%

Crowdsourcing Logistics Pricing Optimization Model Based on DBSCAN Clustering Algorithm

et al. 2020

IEEE Access

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From the perspective of platform economics, crowdsourcing is a very efficient business model, and the pricing of crowdsourcing tasks is a key factor for the sustainable development of the crowdsourcing model. In the logistics industry, crowdsourcing provides a new idea of sustainable development for logistics enterprises, and reasonable distribution pricing is the key to achieving sustainable development. This paper innovatively adds dynamic and decentralized characteristics of logistics on the basis of a detailed analysis of pricing methods and uses this as a basis to build a pricing model. First, based on existing crowdsourced photography task pricing data, this paper establishes a project-centric domain and builds metrics into the attributes of each project based on the data in that domain. Then, a regression model is used to fit the completion rate of previous projects, and a multiple linear regression and optimal pricing mechanism are established. Finally, the DBSCAN algorithm is used to cluster areas with a high project density, and a pricing optimization model based on polynomial Logit (MNL) is established. We found through the model analysis that the optimized pricing strategy of crowdsourcing logistics services has a better packaging completion rate based on a combination of complex factors including bundling and outliers. In short, the main contributions of this paper are to build a complex mathematical model for crowdsourcing tasks, improve the algorithmic deficiencies of the previous crowdsourcing task pricing methods, and provide a reference for further research on crowdsourcing tasks. INDEX TERMS Crowdsourcing logistics, pricing optimization model, DBSCAN clustering algorithm, sustainable development.

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Binomial convolution and transformations of Appell polynomials

Cited by 16 publications

References 34 publications

Appell and Sheffer sequences: on their characterizations through functionals and examples

Appell and Sheffer sequences: on their characterizations through functionals and examples

Explicit expressions and integral representations for the Stirling numbers. A probabilistic approach

Crowdsourcing Logistics Pricing Optimization Model Based on DBSCAN Clustering Algorithm

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