R. B. ParisDivision of Mathematical Sciences,
University of Abertay Dundee,
Dundee, United Kingdom.
This chapter is based in part on
Abramowitz and Stegun (1964, Chapter 12) by M. Abramowitz.
The author is indebted to Adri Olde Daalhuis for correcting
a long-standing error in Eq. (11.10.23) in previous literature.
The main references used in writing this chapter are
Babister (1967, Chapter 3) and Watson (1944, Chapter 10).
For additional bibliographic reading see Erdélyi et al. (1953b, §7.5),
Luke (1969b), Luke (1975, Chapter 10),
Magnus et al. (1966, §3.10), and Olver (1997b).