Results 1 to 10 of about 12,776,695 (181)
Umbral Methods and Harmonic Numbers [PDF]
Axioms, 2018 The theory of harmonic-based functions is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the properties of Gaussian integrals.
Giuseppe Dattoli +3 more
doaj +15 more sources
Dual Numbers and Operational Umbral Methods [PDF]
Axioms, 2019 Dual numbers and their higher-order version are important tools for numerical computations, and in particular for finite difference calculus. Based on the relevant algebraic rules and matrix realizations of dual numbers, we present a novel point of view,
Nicolas Behr +3 more
doaj +10 more sources
q-Functions and Distributions, Operational and Umbral Methods [PDF]
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
doaj +13 more sources
Special Numbers and Polynomials Including Their Generating Functions in Umbral Analysis Methods [PDF]
Axioms, 2018 In this paper, by applying umbral calculus methods to generating functions for the combinatorial numbers and the Apostol type polynomials and numbers of order k, we derive some identities and relations including the combinatorial numbers, the Apostol ...
Yilmaz Simsek
doaj +6 more sources
Integrals of Special Functions and Umbral Methods [PDF]
International Journal of Applied and Computational Mathematics, 2021 AbstractWe derive integrals of combination of Gauss and Bessel functions, by the use of umbral techniques. We show that the method allows the possibility of pursuing new and apparently fruitful avenues in the theory of special functions, displaying interesting links with the theory and the formalism of integral transforms.
Dattoli G. +3 more
exaly +8 more sources
From Circular to Bessel Functions: A Transition through the Umbral Method [PDF]
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
doaj +7 more sources
Voigt Transform and Umbral Image
Mathematical and Computational Applications, 2020 In this paper, we show that the use of methods of an operational nature, such as umbral calculus, allows achieving a double target: on one side, the study of the Voigt function, which plays a pivotal role in spectroscopic studies and in other ...
Silvia Licciardi +3 more
doaj +3 more sources
Umbral Methods, Function Factorisation and Mittag–Leffler Fourier-Type Integral Transform
AxiomsWe propose a systematic way to construct trigonometric-like functions beyond the classical sine–cosine pair by factorising rational expressions in the umbral operator and then evaluating their action on the vacuum.
Giuseppe Dattoli +2 more
doaj +2 more sources
Arquivos Brasileiros de Cardiologia, 2010 FUNDAMENTO: Apesar de o limiar anaeróbio (LAn) ser utilizado na avaliação funcional de diferentes populações, estudos comparando métodos para sua identificação em diabéticos tipo-2 tem sido pouco realizados. OBJETIVO: Comparar protocolos de identificação
Herbert G. Simões +3 more
doaj +2 more sources
Operational Versus Umbral Methods and the Borel Transform [PDF]
International Journal of Applied and Computational Mathematics, 2017 Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms of the Borel type and the associated formalism is shown to be a very effective mean, constituting a solid bridge ...
Dattoli, G. +5 more
openaire +3 more sources