Zobrazeno 1 - 10
of 4 871
pro vyhledávání: '"Segura, J"'
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
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:
Segura, J.
Publikováno v:
J. Math. Anal. Appl. 526(1) (2023) 127211
The best bounds of the form $B(\alpha,\beta,\gamma,x)=(\alpha+\sqrt{\beta^2+\gamma^2 x^2})/x$ for ratios of modified Bessel functions are characterized: if $\alpha$, $\beta$ and $\gamma$ are chosen in such a way that $B(\alpha,\beta,\gamma,x)$ is a s
Externí odkaz:
http://arxiv.org/abs/2207.02713
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 this paper, we give new and complete asymptotic expansions for the rel
Externí odkaz:
http://arxiv.org/abs/2108.11210
Publikováno v:
In Construction and Building Materials 3 May 2024 426
Publikováno v:
In Applied Numerical Mathematics March 2024 197:230-242
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 slowly varying coefficient functions. The sharpness of the bounds is il
Externí odkaz:
http://arxiv.org/abs/2009.04666
Iterative methods with certified convergence for the computation of Gauss--Jacobi quadratures are described. The methods do not require a priori estimations of the nodes to guarantee its fourth-order convergence. They are shown to be generally faster
Externí odkaz:
http://arxiv.org/abs/2008.08641
The classical orthogonal polynomials (Hermite, Laguerre and Jacobi) are involved in a vast number of applications in physics and engineering. When large degrees $n$ are needed, the use of recursion to compute the polynomials is not a good strategy fo
Externí odkaz:
http://arxiv.org/abs/2004.05038
The computation and inversion of the binomial and negative binomial cumulative distribution functions play a key role in many applications. In this paper, we explain how methods used for the central beta distribution function (described in [2]) can b
Externí odkaz:
http://arxiv.org/abs/2001.03953