T. M. Dunster, A. Gil, D. Ruiz-Antolin, J. Segura
Published 2024-07-18Version 1
The real and complex zeros of the parabolic cylinder function $U(a,z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and these are valid for $a$ positive or negative and large in absolute value, uniformly for unbounded $z$ (real or complex). The accuracy of the approximations of the complex zeros is then demonstrated with some comparative tests using a highly precise numerical algorithm for finding the complex zeros of the function.
Uniform asymptotic expansions for the Whittaker functions $M_{κ,μ}(z)$ and $W_{κ,μ}(z)$ with $μ$ large
Uniform asymptotic expansions for Laguerre polynomials and related confluent hypergeometric functions
Uniform asymptotic expansions for Lommel, Anger-Weber and Struve functions
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