Mathematical Methods for Physicists

Babusci, D.; Dattoli, G.; Licciardi, Silvia; Sabia, E.

doi:10.1142/11315

Cited by 38 publications

(55 citation statements)

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“…This is thus consistent with the result calculated via the Zassenhaus-type formula (A6). A detailed proof of the Berry-type identity (A7) independent of the Zassenhaus expansion may also be found in [17,22].…”

Section: Appendix B An Alternative To the Zassenhaus Formulamentioning

confidence: 85%

Operator Ordering and Solution of Pseudo-Evolutionary Equations

Behr

Dattoli

Lattanzi

2019

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The solution of pseudo initial value differential equations, either ordinary or partial (including those of fractional nature), requires the development of adequate analytical methods, complementing those well established in the ordinary differential equation setting. A combination of techniques, involving procedures of umbral and of operational nature, has been demonstrated to be a very promising tool in order to approach within a unifying context non-canonical evolution problems. This article covers the extension of this approach to the solution of pseudo-evolutionary equations. We will comment on the explicit formulation of the necessary techniques, which are based on certain timeand operator ordering tools. We will in particular demonstrate how Volterra-Neumann expansions, Feynman-Dyson series and other popular tools can be profitably extended to obtain solutions of fractional differential equations. We apply the method to a number of examples, in which fractional calculus and a certain umbral image calculus play a role of central importance.

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Section: Appendix B An Alternative To the Zassenhaus Formulamentioning

confidence: 85%

Operator Ordering and Solution of Pseudo-Evolutionary Equations

Behr

Dattoli

Lattanzi

2019

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“…p = 0; q = 0; z = 0 [8] n! n r=0 generalisation, which provides a direct method for the evaluation of this class of integrals [4,5].…”

Section: Special Casesmentioning

confidence: 99%

Identities involving 3-variable Hermite polynomials arising from umbral method

et al. 2020

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“…the modified Bessel functions of first kind. We underline that in [2,5,6], by using theĉ-operator introduced in the following in Equation 18, the K ν (x) and I ν (x) umbral images were provided:…”

Section: Proposition 2 (Noh-integral Representation)mentioning

confidence: 99%

“…Proof. Let us note that the V-transform can be viewed as a generalized form of transform involving the Gamma function (see Chapter 2.7 in [5]) by using of the identity:…”

Section: Corollarymentioning

confidence: 99%

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Voigt Transform and Umbral Image

Licciardi

Pidatella

Artioli

et al. 2020

MCA

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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 applications, according to a new point of view, and on the other, the introduction of a Voigt transform and its possible use. Furthermore, by the same method, we point out that the Hermite and Laguerre functions, extension of the corresponding polynomials to negative and/or real indices, can be expressed through a definition in a straightforward and unified fashion. It is illustrated how the techniques that we are going to suggest provide an easy derivation of the relevant properties along with generalizations to higher order functions.

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Mathematical Methods for Physicists

Cited by 38 publications

References 0 publications

Operator Ordering and Solution of Pseudo-Evolutionary Equations

Operator Ordering and Solution of Pseudo-Evolutionary Equations

Identities involving 3-variable Hermite polynomials arising from umbral method

Voigt Transform and Umbral Image

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