§14.32 Methods of Computation
- Keywords:
- Ferrers functions, associated Legendre functions
- Referenced by:
- ¶ ‣ §3.10(iii)
- Permalink:
- http://dlmf.nist.gov/14.32
Essentially the same comments that are made in §15.19 concerning the
computation of hypergeometric functions apply to the functions described in the
present chapter. In particular, for small or moderate values of the parameters
and 
the power-series expansions of the various hypergeometric
function representations given in §§14.3(i)–14.3(iii),
14.19(ii), and 14.20(i) can be
selected in such a way that convergence is stable, and reasonably rapid,
especially when the argument of the functions is real. In other cases
recurrence relations (§14.10) provide a powerful method when
applied in a stable direction (§3.6); see Olver and Smith (1983)
and Gautschi (1967).
Other methods include:
Application of the uniform asymptotic expansions for large values of the parameters given in §§14.15 and 14.20(vii)–14.20(ix).