T. M. Dunster

activity

20142026

most citedFundamental Solutions and Gegenbauer Expansions of Helmholtz Operators in Riemannian Spaces of Constant Curvature

14 citations · 20 across the 31 of their papers we have counts for

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5 papers · 1 filter

math.NA2024

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 $U (a, z)$ in domains of the complex plane is presented. The algorithm uses a…

math.CA2024

Uniform asymptotic expansions for Bessel functions of imaginary order and their zeros

T. M. Dunster

Bessel and modified Bessel functions of imaginary order $i ν$ ( $ν > 0$ ) are studied. Asymptotic expansions are derived as $ν \to \infty$ that are uniformly valid in unbounded complex d…

math.CA2024

Simplified uniform asymptotic expansions for associated Legendre and conical functions

T. M. Dunster

Asymptotic expansions are derived for associated Legendre functions of degree $ν$ and order $μ$ , where one or the other of the parameters is large. The expansions are uniformly val…

math.CA2024

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 $U (a, z)$ are studied. Asymptotic expansions for the zeros are derived, involving the zeros of Airy functions, and thes…

math.CA2024

Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function $J_{ν} (x)$

T. M. Dunster

A recent asymptotic expansion for the positive zeros $x = j_{ν, m}$ ( $m = 1, 2, 3, \dots$ ) of the Bessel function of the first kind $J_{ν} (x)$ is studied, where the order $ν$ is positive. U…

A numerical algorithm for computing the zeros of parabolic cylinder functions in the complex plane

Uniform asymptotic expansions for Bessel functions of imaginary order and their zeros

Simplified uniform asymptotic expansions for associated Legendre and conical functions

Uniform asymptotic expansions for the zeros of parabolic cylinder functions

Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function Jν​(x)

Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function $J_{ν} (x)$