131 citations · 571 across the 40 of their papers we have counts for
18 papers · 1 filter
The Havriliak-Negami and Jurlewicz-Weron-Stanislavsky relaxation models revisited: memory functions based study
K. Górska, A. Horzela, K. A. Penson
We provide a review of theoretical results concerning the Havriliak-Negami (HN) and the Jurlewicz-Weron-Stanislavsky (JWS) dielectric relaxation models. We derive explicit forms of…
The Volterra type equations related to the non-Debye relaxation
K. Górska, A. Horzela
We investigate a possibility to describe the non-Debye relaxation processes using the Volterra-type equations with kernels given by the Prabhakar functions with the upper parameter…
On the Sheffer-type polynomials related to the Mittag-Leffler functions: applications to fractional evolution equations
K. Górska, A. Horzela, K. A. Penson +1
We present two types of polynomials related to the Mittag-Leffler function namely the fractional Hermite polynomial and the Mittag-Leffler polynomial. The first modifies the Hermit…
On the complete monotonicity of the three parameter generalized Mittag-Leffler function
K. Górska, A. Horzela, A. Lattanzi +1
Using the Bernstein theorem we give a simple proof of the complete monotonicity of the three parameter generalized Mittag-Leffler function for and suita…
Coherence, squeezing and entanglement -- an example of peaceful coexistence
K. Górska, A. Horzela, F. H. Szafraniec
After exhaustive inspection of bosonic coherent states appearing in physical literature two of us, Horzela and Szafraniec, came in 2012 to the reasonably general definition which r…
Mittag-Leffler function and fractional differential equations
K. Górska, A. Lattanzi, G. Dattoli
We adopt a procedure of operational-umbral type to solve the -dimensional fractional Fokker-Planck equation in which time fractional derivative of order () is…
Comments on the Properties of Mittag-Leffler Function
Giuseppe Dattoli, Katarzyna Gorska, Andrzej Horzela +2
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to de…
Theory of relativistic heat polynomials and one-sided Lévy distributions
G. Dattoli, K. Górska, A. Horzela +2
The theory of pseudo-differential operators is a powerful tool to deal with differential equations involving differential operators under the square root sign. These type of equati…
Relativistic Heat Equation via Lévy stable distributions: Exact Solutions
K. A. Penson, K. Górska, A. Horzela +1
We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corr…
On the properties of Laplace transform originating from one-sided Lévy stable laws
K. A. Penson, K. Górska
We consider the conventional Laplace transform of , denoted by with . For $0…
Lacunary Generating Functions for the Laguerre Polynomials
D. Babusci, G. Dattoli, K. Gorska +1
Symbolic methods of umbral nature play an important and increasing role in the theory of special functions and in related fields like combinatorics. We discuss an application of th…
Exact and explicit evaluation of Brezin-Hikami kernels
K. Gorska, K. A. Penson
We present exact and explicit form of the kernels appearing in the theory of energy correlations in the ensembles of Hermitian random matrices with Gaussian probabil…
Generating Functions for Laguerre Polynomials: New Identities for Lacunary Series
D. Babusci, G. Dattoli, K. Gorska +1
We present a number of identities involving standard and associated Laguerre polynomials. They include double-, and triple-lacunary, ordinary and exponential generating functions o…
Symbolic methods for the evaluation of sum rules of Bessel functions
D. Babusci, G. Dattoli, K. Gorska +1
The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way…
On Mittag-Leffler function and associated polynomials
D. Babusci, G. Dattoli, K. Górska
The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connec…
Levy stable distributions via associated integral transform
K. Gorska, K. A. Penson
We present a method of generation of exact and explicit forms of one-sided, heavy-tailed Levy stable probability distributions g_α(x), 0 \leq x < \infty, 0 < α< 1. We demonstrate t…
The Ramanujan master theorem and its implications for special functions
K. Gorska, D. Babusci, G. Dattoli +2
We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure f…
Quasiclassical Asymptotics and Coherent States for Bounded Discrete Spectra
K. Gorska, K. A. Penson, A. Horzela +3
We consider discrete spectra of bound states for non-relativistic motion in attractive potentials V_σ(x) = -|V_{0}| |x|^{-σ}, 0 < σ\leq 2. For these potentials the quasiclassical a…