Asymptotic and computational analysis. Conference in honor of Frank W.J. Olver’s 65th birthday, Proc. Int. Symp., Winnipeg/Can. 1989, Lect. Notes Pure Appl. Math. 124, 53-73 (1990).
[For the entire collection see Zbl 0689.00009.]
The author considers uniform asymptotic expansions as of solutions to the differential equation
where , () is holomorphic in a certain simply-connected domain and . The method is described in F. W. J. Olver’s book [Asymptotics and special functions (1974; Zbl 0303.41035) ch. 12]. For the coefficients of these expansions recurrence formulas are given. Error bounds for the remainders are constructed by means of a Volterra integral equation. As an application expansions for Legendre functions and , , , , are given.