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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math.CA2026

Whittaker functions with one or both parameters large: simplified uniform asymptotic expansions involving Bessel and Airy functions

T. M. Dunster

Uniform asymptotic expansions are derived as $κ \to \infty$ for the Whittaker functions $W_{κ, μ} (z)$ , $M_{κ, μ} (z)$ , as well as related functions including generalized Laguerre polyn…

math.CA2026

The general Brannan coefficient conjecture II: Meijer-function approximations

T. M. Dunster

The coefficients $A_{n} (α, β, ω)$ in the Maclaurin expansion $(1 + ω z)^{α} (1 - z)^{- β} = \sum_{n = 0}^{\infty} A_{n} (α, β, ω) z^{n}$ are considered for $∣ ω ∣ = 1$ and $α, β \in (0, 1]$ . D. A. Brannan conjectu…

math.CA2026

The general Brannan coefficient conjecture I: Watson-lemma approximations

T. M. Dunster

The coefficients $A_{n} (α, β, ω)$ in the Maclaurin expansion $(1 + ω z)^{α} (1 - z)^{- β} = \sum_{n = 0}^{\infty} A_{n} (α, β, ω) z^{n}$ are studied, where $ω, z \in C$ with $∣ z ∣ < ∣ ω ∣ = 1$ , and $α,…