§31.13 Asymptotic Approximations

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Keywords:: Heun functions, Heun’s equation, accessory parameter, asymptotic approximations, confluent forms, eigenvalues of accessory parameters, solutions near irregular singularities, solutions of confluent forms, solutions with coalescing singularities
Permalink:: http://dlmf.nist.gov/31.13
See also:: Annotations for Ch.31

For asymptotic approximations for the accessory parameter eigenvalues $q_{m}$ , see Fedoryuk (1991) and Slavyanov (1996).

For asymptotic approximations of the solutions of Heun’s equation (31.2.1) when two singularities are close together, see Lay and Slavyanov (1999).

For asymptotic approximations of the solutions of confluent forms of Heun’s equation in the neighborhood of irregular singularities, see Komarov et al. (1976), Ronveaux (1995, Parts B,C,D,E), Bogush and Otchik (1997), Slavyanov and Veshev (1997), and Lay et al. (1998).