The remaining radial dependency follows by inserting spectral domain field function [mathematical expression not reproducible] into (1) which is then reduced to Bessel
's differential equation describing radial transmission line [9, 10].
The incident beam can be Gaussian, Bessel
, or other kinds of beams.
with [j.sub.n](z) and [h.sup.(1).sub.n](z) being the spherical Bessel
functions of the first and the third kind, respectively.
[I.sub.m] (x) is an mth order modified Bessel
function of first kind and it can be written as 
In this paper, we consider the so-called gambler's ruin problem for a discrete-time Markov chain that converges to a Bessel
This normalized and generalized Bessel
function of the first kind of order p also satisfies the following recurrence relation:
Motivated by results on connection between various subclasses of analytic functions by using the hypergeometric function by many author particularly the authors (see- ) and generalized Bessel
functions (see - ), S.Porrwal  obtained the necessary and sufficient conditions for a functions ( , ) F m z defined by using the poisson distribution belong to the class ( , ) T and ( , ) C .
The Alexander von Humboldt Foundation grants approximately 20 Friedrich Wilhelm Bessel
Research Awards annually to internationally renowned scholars in recognition for their outstanding accomplishments in research and their exceptional promise to the future.
Figure 2 shows the effect of the upper cutoff frequency [f.sub.2] of the fourth order Bessel
BPF on the characteristics of the ECG signal of P-44 in the vicinity of QRS complex, [f.sub.1] = 0.01 Hz.
Appendices include physical properties of relevant materials and Bessel
Selectable analog filtering includes a seven-pole Bessel
characteristic -3 dB down at about 200 kHz for time-domain applications requiring an optimal step response and a seven-pole Butterworth shape -3 dB down at about 300 kHz for the flattest and widest frequency response.
where [J.sub.m]([[lambda].sup.p.sub.j]x) denotes the mth-order Bessel
function of the first kind and m corresponds to the circumferential mode.
The Hankel transforms (HT) arise naturally in the discussion of problems posedin cylindrical coordinates and hence 1], as a result of separation of variables, involving Bessel
The formal solution of (3) can be easily expressed in terms of Bessel