…
►
…
►If, as
, the wanted solution
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
…
►Subsequently, 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.
…
►A 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.
►A fourth
method is by asymptotic approximations by zeros of orthogonal polynomials of increasing degree.
…
§7.22 Methods of Computation
…
►The
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.
…
►The
recursion scheme given by (
7.18.1) and (
7.18.7) can be used for computing
.
See
Gautschi (1977a), where forward and
backward recursions are used; see also
Gautschi (1961).
…
►For a comprehensive survey of computational
methods for the functions treated in this chapter, see
van der Laan and Temme (1984, Ch. V).