…

βΊ
…

βΊIf, as

$n\to \mathrm{\infty}$, the wanted solution

${w}_{n}$ grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (

backward)

recursion is stable.
…

######
§29.20 Methods of Computation

…

βΊSubsequently, formulas typified by (

29.6.4) can be applied to compute the coefficients of the Fourier expansions of the corresponding Lamé functions by

backward recursion followed by application of formulas typified by (

29.6.5) and (

29.6.6) to achieve normalization; compare §

3.6.
…

βΊA third

method is to approximate eigenvalues and Fourier coefficients of Lamé functions by eigenvalues and eigenvectors of finite matrices using the

methods of §§

3.2(vi) and

3.8(iv).
…The numerical computations described in

Jansen (1977) are based in part upon this

method.

βΊA fourth

method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree.
…

######
§7.22 Methods of Computation

…

βΊThe

methods available for computing the main functions in this chapter are analogous to those described in §§

6.18(i)–

6.18(iv) for the exponential integral and sine and cosine integrals, and similar comments apply.
…

βΊThe

recursion scheme given by (

7.18.1) and (

7.18.7) can be used for computing

${\mathrm{i}}^{n}\beta \x81\u2019\mathrm{erfc}\beta \x81\u2018\left(x\right)$.
See

Gautschi (1977a), where forward and

backward recursions are used; see also

Gautschi (1961).
…

βΊFor a comprehensive survey of computational

methods for the functions treated in this chapter, see

van der Laan and Temme (1984, Ch. V).