5 papers
Uniform Asymptotic approximation and numerical evaluation of the Reverse Generalized Bessel Polynomial zeros
T. M. Dunster, Amparo Gil, Diego Ruiz-Antolin +1
Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree and real parameter . It is assumed that $-Δ_{1} n+\frac…
A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane
T. M. Dunster, A. Gil, D. Ruiz-Antolín +1
A numerical algorithm (implemented in Matlab) for computing the zeros of the parabolic cylinder function in domains of the complex plane is presented. The algorithm uses a…
Uniform asymptotic expansions for the zeros of parabolic cylinder functions
T. M. Dunster, A. Gil, D. Ruiz-Antolin +1
The real and complex zeros of the parabolic cylinder function are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and thes…
Complete asymptotic expansions for the relativistic Fermi-Dirac integral
A. Gil, J. Segura, N. M. Temme
Fermi-Dirac integrals appear in problems in nuclear astrophysics, solid state physics or in the fundamental theory of semiconductor modeling, among others areas of application. In…
Sharp error bounds for turning point expansions
T. M. Dunster, A. Gil, J. Segura
Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and s…