Zobrazeno 1 - 10
of 102
pro vyhledávání: '"Dunster, T. M."'
Autor:
Dunster, T. M.
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are are uniformly valid for unbounded real and complex values of the argument $z$,
Externí odkaz:
http://arxiv.org/abs/2410.03002
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,
Externí odkaz:
http://arxiv.org/abs/2407.13936
Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function $J_{\nu}(x)$
Autor:
Dunster, T. M.
A recent asymptotic expansion for the positive zeros $x=j_{\nu,m}$ ($m=1,2,3,\ldots$) of the Bessel function of the first kind $J_{\nu}(x)$ is studied, where the order $\nu$ is positive. Unlike previous well-known expansions in the literature, this i
Externí odkaz:
http://arxiv.org/abs/2405.08208
Autor:
Dunster, T. M.
Reformulated uniform asymptotic expansions are derived for ordinary differential equations having a large parameter and a simple turning point. These involve Airy functions, but not their derivatives, unlike traditional asymptotic expansions. From th
Externí odkaz:
http://arxiv.org/abs/2310.16016
Numerical methods for the computation of the parabolic cylinder $U(a,z)$ for real $a$ and complex $z$ are presented. The main tools are recent asymptotic expansions involving exponential and Airy functions, with slowly varying analytic coefficient fu
Externí odkaz:
http://arxiv.org/abs/2210.16982
Autor:
Dunster, T. M.
Asymptotic expansions are derived for Gegenbauer (ultraspherical) polynomials for large order $n$ that are uniformly valid for unbounded complex values of the argument $z$, including the real interval $0 \leq z \leq 1$ in which the zeros are located.
Externí odkaz:
http://arxiv.org/abs/2209.10716
Autor:
Dunster, T. M., Perez, Jessica M.
The function $g(x)= (1+1/x)^{x}$ has the well-known limit $e$ as $x\rightarrow{\infty}$. The coefficients $c_{j}$ in an asymptotic expansion for $g(x)$ are considered. A simple recursion formula is derived, and then using Cauchy's integral formula th
Externí odkaz:
http://arxiv.org/abs/2105.03794
Autor:
Dunster, T. M.
Uniform asymptotic expansions are derived for Whittaker's confluent hypergeometric functions $M_{\kappa,\mu}(z)$ and $W_{\kappa,\mu}(z)$, as well as the numerically satisfactory companion function $W_{-\kappa,\mu}(ze^{-\pi i})$. The expansions are un
Externí odkaz:
http://arxiv.org/abs/2104.12912
Autor:
Dunster, T. M.
Using a differential equation approach asymptotic expansions are rigorously obtained for Lommel, Weber, Anger-Weber and Struve functions, as well as Neumann polynomials, each of which is a solution of an inhomogeneous Bessel equation. The approximati
Externí odkaz:
http://arxiv.org/abs/2104.01700
Autor:
Dunster, T. M.
Nield-Kuznetsov functions of the first kind are studied, which are solutions of an inhomogeneous parabolic Weber equation, and have applications in fluid flow problems. Connection formulas are constructed between them, numerically satisfactory soluti
Externí odkaz:
http://arxiv.org/abs/2102.11322