For expansions of arbitrary functions in series of
Mκ,μ(z) functions see Schäfke (1961b).
For z∈ℂ, and again with the notation of §§10.2(ii)
where p0(μ)(z)=1, p1(μ)(z)=16z2, and
higher polynomials ps(μ)(z) are defined by
(13.18.8) is a special case of (13.24.1).
Additional expansions in terms of Bessel functions are given in
Luke (1959). See also López (1999).
For other series expansions see
Prudnikov et al. (1990, §6.6). See also §13.26.