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Bessel functions and Weyl's law for balls and spherical shells

Bessel functions and Weyl's law for balls and spherical shells

The purpose of this paper is twofold. One is to investigate the properties of the zeros of cross-products of Bessel functions or derivatives of ultraspherical Bessel functions, as well as the properties of the zeros of the derivative of the first-kind ultraspherical Bessel function. The properties we study include asymptotics …