T. M. Dunster

collaborators

12 papers

math.CA2026

The general Brannan coefficient conjecture II: Meijer-function approximations

T. M. Dunster

The coefficients $A_{n} (I^\pm, I^^{2}, I ¨ )$ in the Maclaurin expansion $(1 + I ¨ z)^{I^} \pm (1 - z)^{- I^^{2}} = \sum_{n = 0}^{\infty} A_{n} (I^\pm, I^^{2}, I ¨ ) z^{n}$ are considered for $∣ I ¨ ∣ = 1$ and $I^\pm, I^^{2} \in (0, 1]$ . D. A. Bran…

math.CA2026

The general Brannan coefficient conjecture I: Watson-lemma approximations

T. M. Dunster

The coefficients $A_{n} (I^\pm, I^^{2}, I ¨ )$ in the Maclaurin expansion $(1 + I ¨ z)^{I^} \pm (1 - z)^{- I^^{2}} = \sum_{n = 0}^{\infty} A_{n} (I^\pm, I^^{2}, I ¨ ) z^{n}$ are studied, where $I ¨ , z \in C$ with $|z| < |Ï|=…

math.CA2025

Asymptotic expansions for solutions of differential equations having a coalescing turning point and double pole, with an application to Legendre functions

T. M. Dunster

The asymptotic behavior of solutions to the second-order linear differential equation $d^{2} w / d z^{2} = {u^{2} f (I^\pm, z) + g (z)} w$ is analyzed for a large real parameter $u$ and $Î±\in[0…

math.CA2025

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 $n$ and real parameter $a$ . It is assumed that $-Î_{1} n+\fra…

math.CA2025

Asymptotic expansions for solutions of differential equations having coalescing turning points, with an application to Legendre functions

T. M. Dunster

Linear second-order ordinary differential equations of the form $d^{2} w / d z^{2} = {u^{2} f (a, z)$ $+ g (z)} w$ are studied for large values of the real parameter $u$ , where $z$ ranges ov…

math.CA2025

Uniform asymptotic expansions for generalised trigonometric integrals and their zeros

T. M. Dunster

Asymptotic expansions for generalised trigonometric integrals are obtained in terms of elementary functions, which are valid for large values of the parameter $a$ and unbounded com…