A Property of Bessel Functions and Its Application to the Theory of Two Rheometers

Abstract

A method of expanding expressions of the type J(ξ)Y(σ)−J(σ)Y(ξ) and J′(ξ)Y(σ)−J′(σ)Y(ξ) is given. Here J and Y are Bessel functions of the first and second kind. These forms occur frequently in physical problems with cylindrical symmetry. The type of expansion used here can be used with other functions that are solutions of second‐order differential equations. The use of these expansions allows the development of theories for two rheometers used for determining dynamic mechanical properties of liquids. In these mathematical treatments, the inertia of the sample is taken into account.