Integrals of Special Functions and Umbral Methods
Sign Up to like & getrecommendations! Published in 2021 at "International Journal of Applied and Computational Mathematics"
DOI: 10.1007/s40819-021-01047-w
Abstract: We 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… read more here.
Keywords: special functions; functions umbral; umbral methods; integrals special ... See more keywords
Dual Numbers and Operational Umbral Methods
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DOI: 10.3390/axioms8030077
Abstract: 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… read more here.
Keywords: numbers operational; operational umbral; dual numbers; umbral methods ... See more keywords
Inverse Derivative Operator and Umbral Methods for the Harmonic Numbers and Telescopic Series Study
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DOI: 10.3390/sym13050781
Abstract: The formalism of differ-integral calculus, initially developed to treat differential operators of fractional order, realizes a complete symmetry between differential and integral operators. This possibility has opened new and interesting scenarios, once extended to positive… read more here.
Keywords: derivative operator; harmonic numbers; operator umbral; series ... See more keywords