Superluminal Behaviour of Modified Bessel Waves

Dynamic Behaviour of Piers Under Waves and Earthquakes

Dynamic Behaviour of Piers Under Waves and Earthquakes

Representation of the Modified Bessel Functions ∗

Some power series representations of the modified Bessel functions (McDonald functions Kα) are derived using the little known formalism of fractional derivatives. The resulting summation formulae are believed to be new. 1 Fractional derivatives There are several non-trivial examples in mathematics when some quantity, originally defined as integer, can radically extend its original range and ass...

Nondiffracting chirped Bessel waves in optical antiguides.

Chirped Bessel waves are introduced as stable (nondiffracting) solutions of the paraxial wave equation in optical antiguides with a power-law radial variation in their index of refraction. Through numerical simulations, we investigate the propagation of apodized (finite-energy) versions of such waves, with or without vorticity, in antiguides with practical parameters. The new waves exhibit a re...

On a Product of Modified Bessel Functions

Let Iν and Kν denote the modified Bessel functions of the first and second kinds of order ν. In this note we prove that the monotonicity of u → Iν(u)Kν(u) on (0,∞) for all ν ≥ −1/2 is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order ν. Moreover, we show that the function u → Iν(u)Kν(u) is strict...