Results 71 to 80 of about 166,207 (201)
More on the umbral calculus, with emphasis on the q-umbral calculus
Journal of Mathematical Analysis and Applications, 1985 AbstractThe interrelationship between distinct umbral calculi is studied. These ideas are applied in particular to q-umbral calculus, which shows how Andrews' q-theory relates to the q-theory discussed in the previous paper by the author. The q-Hermite polynomials and basic hypergeometric series are briefly discussed.
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From Circular to Bessel Functions: A Transition through the Umbral Method
Fractal and Fractional, 2017 A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions.
Giuseppe Dattoli +3 more
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A new approach to the r-Whitney numbers by using combinatorial differential calculus
Acta Universitatis Sapientiae: Mathematica, 2019 In the present article we introduce two new combinatorial interpretations of the r-Whitney numbers of the second kind obtained from the combinatorics of the differential operators associated to the grammar G := {y → yxm, x → x}.
Méndez Miguel A., Ramírez José L.
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A Family of Generalized Legendre-Based Apostol-Type Polynomials
Axioms, 2022 Numerous polynomials, their extensions, and variations have been thoroughly explored, owing to their potential applications in a wide variety of research fields.
Talha Usman +3 more
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Integration in the umbral calculus
Journal of Mathematical Analysis and Applications, 1980 AbstractThe adjointness between “multiplication” and “derivation” is a recurrent theme in Rota's umbral calculus. The subject of this paper is the companion adjointness between “division” and “integration.”
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Equine Veterinary Journal, Volume 57, Issue 3, Page 645-653, May 2025.Abstract Background Equine trigeminal‐mediated (TGM) headshaking (HS) is a neuropathic facial pain syndrome characterised by varying intensity and frequencies of head movements and signs of nasal irritation. An accurate method for quantification and/or characterisation of HS severity is lacking.
Kirstie Jane Pickles +3 more
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Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials
Mathematics, 2019 In recent years, intensive studies on degenerate versions of various special numbers and polynomials have been done by means of generating functions, combinatorial methods, umbral calculus, p-adic analysis and differential equations.
Taekyun Kim, Dae San Kim
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Certain Hybrid Matrix Polynomials Related to the Laguerre-Sheffer Family
Fractal and Fractional, 2022 The main goal of this article is to explore a new type of polynomials, specifically the Gould-Hopper-Laguerre-Sheffer matrix polynomials, through operational techniques.
Tabinda Nahid, Junesang Choi
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Threats posed by land use to water quality in South Africa's strategic water source areas
World Water Policy, Volume 11, Issue 1, Page 155-164, February 2025.Abstract Understanding the negative impacts of land use/land cover (LULC) on water quality is key to developing effective integrated catchment management strategies. However, in line with the Integrated Water Resources Management (IWRM) philosophy, this necessitates the generation and application of useful scientific knowledge, which stakeholders and ...
Kent Anson Locke, Kevin Winter
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Bell-Based Bernoulli Polynomials with Applications
Axioms, 2021 In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind.
Ugur Duran, Serkan Araci, Mehmet Acikgoz
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