Analytic approximation to Bessel function $$J_{0}(x)$$

Bessel Function Zeroes

0  1  2  3   as does its derivative  0 (): 0  0 1   0 2   0 3     0 0 = 0 01   0 02   0 03   0 04    = 0 See Tables 1 & 2 for the cases  = 0 1 2 and Tables 3 & 4 for the cases  = 12 32 52. These appear in many physical applications that we cannot hope to survey in entirety. We will state only a few properties and several importan...

A Bessel Function Multiplier

We obtain nearly sharp estimates for the L p (R 2) norms of certain convolution operators. For n 1 let n be the measure on R 2 obtained by multiplying normalized arclength measure on fjxj = 1g by the oscillating factor e inarg(x). For 1 p 1, let C(p; n) denoted the norm of the operator T n f : = n f on L p (R 2). The purpose of this note is to estimate the rate of decay of C(p; n) as n ! 1. By ...

Approximation of Bessel Beams with Annular Arrays

1 Abstract — It is shown that the limited-diffraction Bessel beam of order zero can be generated by a transducer with equal-area division of elements and with a fixed prefocus, i.e. conventional transducers used in medical imaging equipment. The element division implies that the scaling parameter must be chosen to contain the first lobe of the Bessel function in the first element. In addition t...

An Analytic Approximation to the Isothermal Sphere

We present a useful analytic approximation to the solution of the Lane-Emden equation for infinite polytropic index the isothermal sphere. The optimized expression obtained for the density profile can be accurate to within 0.04% within 5 core-radii and to 0.1% within 10 core-radii.

Analytic Approximation Theorem