Independent solutions of (31.2.1) can be computed in the
neighborhoods of singularities from their Fuchs–Frobenius expansions
(§31.3), and elsewhere by numerical integration of
(31.2.1). Subsequently, the coefficients in the necessary
connection formulas can be calculated numerically by matching the values of
solutions and their derivatives at suitably chosen values of 
; see
Laĭ (1994) and Lay et al. (1998). Care needs to be taken to choose
integration paths in such a way that the wanted solution is growing in
magnitude along the path at least as rapidly as all other solutions
(§3.7(ii)). The computation of the accessory parameter for
the Heun functions is carried out via the continued-fraction equations
(31.4.2) and (31.11.13) in the same way as for the
Mathieu, Lamé, and spheroidal wave functions in
Chapters 28–30.
