Search results for "Bessel function"
showing 10 items of 61 documents
Free-space delay lines and resonances with ultraslow pulsed Bessel beams
2008
We investigate the ultraslow motion of polychromatic Bessel beams in unbounded, nondispersive media. Control over the group velocity is exercised by means of the angular dispersion of pulsed Bessel beams of invariant transverse spatial frequency, which spontaneously emerge from near-field generators. Temporal dynamics in transients and resonances over homogeneous delay lines (dielectric slabs) are also examined.
Analytical formulation of the axial behavior of apodized general Bessel beams
1999
We present an analytical formula for the evaluation of the axial-irradiance distribution of general Bessel beams apodized by a radially-nonsymmetric window. Our approach is based on the similarity between the axial behavior of such beams and the propagation properties of a properly modified version of the window transmittance. To illustrate our formalism, we analyze the axial behavior of some complex beams.
Forces Between Thin Coils With Parallel Axes Using Bessel Functions
2013
A method based on Bessel functions is presented for calculating the forces between combinations of thin coils with parallel axes. The coaxial case is solved in closed form in terms of elliptic integrals, whereas for the noncoaxial case the force components are expressed both as integrals of Bessel functions and as integrals of complete elliptic integrals. The results for the coaxial case have been compared with calculations in the literature with excellent agreement. The numerical results presented for the noncoaxial have been cross-checked by comparing the two methods. These methods can also be applied to current loops, disk coils, thick noncoaxial cylindrical coils, and various combinatio…
Indefinite integrals of quotients of Gauss hypergeometric functions
2018
A method recently applied to obtain indefinite integrals involving quotients of some common special functions is applied to obtain indefinite integrals of some quotients of Gauss hypergeometric fun...
Indefinite integrals of quotients of special functions
2018
ABSTRACTA new method is presented for deriving indefinite integrals involving quotients of special functions. The method combines an integration formula given previously with the recursion relations obeyed by the function. Some additional results are presented using an elementary method, here called reciprocation, which can also be used in combination with the new method to obtain additional quotient integrals. Sample results are given here for Bessel functions, Airy functions, associated Legendre functions and the three complete elliptic integrals. All results given have been numerically checked with Mathematica.
On some dual frames multipliers with at most countable spectra
2021
A dual frames multiplier is an operator consisting of analysis, multiplication and synthesis processes, where the analysis and the synthesis are made by two dual frames in a Hilbert space, respectively. In this paper we investigate the spectra of some dual frames multipliers giving, in particular, conditions to be at most countable. The contribution extends the results available in literature about the spectra of Bessel multipliers with symbol decaying to zero and of multipliers of dual Riesz bases.
New special function recurrences giving new indefinite integrals
2018
ABSTRACTSequences of new recurrence relations are presented for Bessel functions, parabolic cylinder functions and associated Legendre functions. The sequences correspond to values of an integer variable r and are generalizations of each conventional recurrence relation, which correspond to r=1. The sequences can be extended indefinitely, though the relations become progressively more intricate as r increases. These relations all have the form of a first-order linear inhomogeneous differential equation, which can be solved by an integrating factor. This gives a very general indefinite integral for each recurrence. The method can be applied to other special functions which have conventional …
Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions
2015
We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the first kind. The coefficients of different expansions obey four-, five-, or six-term recurrence relations that are reduced to ones involving less number of terms only in a few exceptional cases. The conditions for deriving finite-sum solutions via termination of the series are discussed.
Frames and representing systems in Fréchet spaces and their duals
2014
[EN] Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.
Bessel sequences, Riesz-like bases and operators in Triplets of Hilbert spaces
2016
Riesz-like bases for a triplet of Hilbert spaces are investigated, in connection with an analogous study for more general rigged Hilbert spaces performed in a previous paper. It is shown, in particular, that every \(\omega \)-independent, complete (total) Bessel sequence is a (strict) Riesz-like basis in a convenient triplet of Hilbert spaces. An application to non self-adjoint Schrodinger-type operators is considered. Moreover, some of the simplest operators we can define by them and their dual bases are studied.