Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit

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Abstract

We construct asymptotic formulae for the approximation of certain prolate spheroidal wave functions and of the corresponding eigenvalues. We investigate two regimes: when the ratio c / m decays, and when both c and m grow, but the ratio c / m stays bounded. Both the regions of validity and the accuracies of the obtained expansions are illustrated with numerical examples. © 2006 Elsevier Inc. All rights reserved.

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Rokhlin, V., & Xiao, H. (2007). Approximate formulae for certain prolate spheroidal wave functions valid for large values of both order and band-limit. Applied and Computational Harmonic Analysis, 22(1), 105–123. https://doi.org/10.1016/j.acha.2006.05.004

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