Luke (1969b, pp. 35 and 25) provides Chebyshev-series expansions of
M(a,b,x) and U(a,b,x) that include the intervals
0≤x≤α and α≤x<∞, respectively, where α
is an arbitrary positive constant.
For a discussion of
the convergence of the Padé approximants that are related to the
continued fraction (13.5.1) see Wimp (1985).
In Luke (1977a) the following rational approximation is given, together with its rate of
convergence. For the notation see §16.2(i).
Let a,a+1-b≠0,-1,-2,…, |phz|<π,