On Sound Reflection in Superfluid

We consider reflection of the first and the second sound waves by a rigid flat wall in superfluid. Nontrivial dependence of the reflection coefficients on the angle of incidence is obtained. Sound conversion is predicted at slanted incidence.Comment: 9 pages, 4 figure

Error bounds for the large-argument asymptotic expansions of the Hankel and Bessel functions

In this paper, we reconsider the large-argument asymptotic expansions of the Hankel, Bessel and modified Bessel functions and their derivatives. New integral representations for the remainder terms of these asymptotic expansions are found and used to obtain sharp and realistic error bounds. We also give re-expansions for these remainder terms and provide their error estimates. A detailed discussion on the sharpness of our error bounds and their relation to other results in the literature is given. The techniques used in this paper should also generalize to asymptotic expansions which arise from an application of the method of steepest descents.Comment: 32 pages, 2 figures, accepted for publication in Acta Applicandae Mathematica

Basic Methods for Computing Special Functions

This paper gives an overview of methods for the numerical evaluation of special functions, that is, the functions that arise in many problems from mathematical physics, engineering, probability theory, and other applied sciences. We consider in detail a selection of basic methods which are frequently used in the numerical evaluation of special functions: converging and asymptotic series, including Chebyshev expansions, linear recurrence relations, and numerical quadrature. Several other methods are available and some of these will be discussed in less detail. We give examples of recent software for special functions where these methods are used. We mention a list of new publications on computational aspects of special functions available on our website

Presidential address

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