We derive completeness criteria for sequences of functions of the form f(xλn), where λn is the nth zero of a suitably chosen entire function. Using these criteria, we construct systems of nonorthogonal Fourier-Bessel functions and their q-analogues, as well as other complete sets of q-special functions. The completeness of certain sets of q-Bessel functions is then used to prove that, if a func...

An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

We report the first experimental realization of all-optical trapping and manipulation of plasmonic nanowires in three dimensions. The optical beam used for trapping is the Fourier transform of a linearly polarized Bessel beam (termed FT-Bessel). The extended depth of focus of this beam enables the use of a retroreflection geometry to cancel radiation pressure in the beam propagation direction, ...

This paper proposes the Fourier-Bessel cepstral coefficients (FBCC) as features for robust text-independent speaker identification. Fourier-Bessel (FB) expansion is used instead of Fourier transform for representing the signal in frequency domain. FB expansion can be viewed as two-dimensional Fourier transform. Change in the kernel of the transform from exponential to decaying exponentials help...

In this paper, we present a systematic study of the various characteristics and properties some continuous discrete fractional Bessel wavelet transforms. The method is based upon theory Hankel transform.

Postnicov [22], in 2003, proposed an algorithm to compute the Hankel transforms of order zero and one by using Haar wavelets. But the proposed method faced problems in the evaluation of zero order Hankel transform. The purpose of this paper is to overcome this problem and obtain an efficient algorithm for evaluating Hankel transform of order zero by using rationalized Haar wavelets. Exact analy...

In this paper we present an explicit (rank one) function transform which contains several Jacobi-type function transforms and Hankel-type transforms as degenerate cases. The kernel of the transform, which is given explicitly in terms of basic hypergeometric series, thus generalizes the Jacobi function as well as the Bessel function. The kernel is named the Askey-Wilson function, since it provid...

In this present study, we investigate the solutions for fractional kinetic equations involving k-Struve function using the Sumudu transform. The graphical interpretations of the solutions involving k-Struve function and its comparison with generalized Bessel function are given. The methodology and results can be considered and applied to various related fractional problems in mathematical physics.