The Kratzel function [Z.sup.v.sub.[rho]](x) is related to the
modified Bessel function of the second kind [K.sub.v] by the relationship
where the free parameter vector is [theta] = [[M t].sup.T], and [K.sub.M-1] denotes the
modified Bessel function of the second kind with the order of M - 1.
[c.sup.2.sub.1] = k/[mu], [c.sup.2.sub.2] = k/([lambda] + 2[mu]), and [K.sub.0] is the
modified Bessel function of the second kind and order zero [2].
where [K.sub.1] is the
modified Bessel function of the second kind and order 1 and [L.sub.n] is the modified Struve function of order n.
where [Sigma](r) is illustrated in Figure 3 and with a homogeneous Dirichlet boundary condition at one end and a Dirichlet condition involving a
modified Bessel function of the second kind of order 0 at the other.
[K.sub.n](v) =
modified Bessel function of the second kind