186 research outputs found
Towards a wave theory of charged beam transport: A collection of thoughts
We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport
Operational Identities and Properties of Ordinary and Generalized Special Functions
AbstractThe theory of Hermite, Laguerre, and of the associated generating functions is reformulated within the framework of an operational formalism. This point of view provides more efficient tools which allow the straightforward derivation of a wealth of new and old identities. In this paper a central role is played by negative derivative operators and by their link with the Tricomi functions and the generalized Laguerre polynomials
Miscellaneous identities of generalized Hermite polynomials
We extend a number of identities valid for the ordinary case to generalized Hermite polynomials with two indices and two variables. These identities, new to the authors knowledge, are obtained by using an operatorial procedure based on the properties of the Weyl group
Theory of multivariable Bessel functions and elliptic modular functions
The theory of multivariable Bessel functions is exploited to establish further links with the elliptic functions. The starting point of the present investigations is the Fourier expansion of the theta functions, which is used to derive an analogous expansion for the Jacobi functions (sn,dn,cn...) in terms of multivariable Bessel functions, which play the role of Fourier coefficients. An important by product of the analysis is an unexpected link with the elliptic modular functions
Theory of multiindex multivariable Bessel functions and Hermite polynomials
We discuss the theory of multivariable multiindex Bessel functions (B.F.) and Hermite polynomials (H.P.) using the generating function method. We derive addition and multiplication theorems and discuss how generalized H.P. can be exploited as a useful complement to the theory of B.F.. We also discuss the importance of the Poisson-Charlier polynomials in the context of multiindex special functions
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
Some families of mixed generating functions and generalized polynomials
The main object of this paper is to show that combined use of the Lagrange expansion and certain operational techniques allows to derive mixed generating functions of various families of generalized polynomials in a straightforward manner. Relevant connections with many other recent works on this subject are also discussed
- …