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...

Keywords: Squared spherical Bessel functions Regularization of Hankel series Gaussian power-law densities Kummer distributions Airy approximation of Bessel integrals a b s t r a c t Bessel integrals of type R 1 0 k lþ2 e Àak 2 ÀðbþixÞk j 2 l ðpkÞdk are studied, where the squared spherical Bessel function j 2 l is averaged with a modulated Gaussian power-law density. These inte-grals define the ...

Introduction/purpose: The aim of this article is to establish integral transforms the generalized Lommel-Wright function. Methods: These are expressed in terms Wright Hypergeometric Results: Integrals involving trigonometric, Bessel function and Struve functions obtained. Conclusions: Various interesting as consequence method

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...