Bessel functions, central to many problems in mathematical physics, provide solutions to differential equations that describe wave propagation, heat conduction and vibrations in cylindrical or ...

An evaluation of the derivative of spherical Bessel functions of order n + 1/2 at its zeros is obtained. Consequently, an explicit quadrature formula for entire functions of exponential type is given.

The JROOT function returns an n ×2 matrix with the calculated roots in the first column and the derivatives in the second column. The inputs to the JROOT function are as follows: is a scalar denoting ...

Bessel beam microscopy, and the techniques that preceded it, are generally used to image live cells in 3D. Bessel beams have a greater capability than other super-resolution imaging techniques for ...

(A) Optical image of the rGO electrode. (B and C) The SEM and EDS observations of the rGO electrode. (D) An optical axis view of the corresponding light intensity distribution of the Bessel beam.