121184 20241125101126.0 doi 10.1111/sapm.12539 sideral 131696 ART-2023-131696 eng Ferreira, Chelo Universidad de Zaragoza (orcid)0000-0002-3698-6719 Asymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals 2023 Access copy available to the general public Unrestricted We consider the highly oscillatory integral () ∶= ∫ ∞ −∞ (+2+) () for large positive values of , − < ≤ , and positive integers with 1 ≤ ≤ , and () an entire function. The standard saddle point method is complicated and we use here a simplified version of this method introduced by López et al. We derive an asymptotic approximation of this integral when → +∞ for general values of and in terms of elementary functions, and determine the Stokes lines. For ≠ 1, the asymptotic behavior of this integral may be classified in four different regions according to the even/odd character of the couple of parameters and ; the special case =1 requires a separate analysis. As an important application, we consider the family of canonical catastrophe integrals Ψ(1, 2,…,) for large values of one of its variables, say , and bounded values of the remaining ones. This family of integrals may be written in the form () for appropriate values of the parameters , and the function (). Then, we derive an asymptotic approximation of the family of canonical catastrophe integrals for large ||. The approximations are accompanied by several numerical experiments. The asymptotic formulas presented here fill up a gap in the NIST Handbook of Mathematical Functions by Olver et al. info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 2.6 2023 MATHEMATICS, APPLIED 28 / 332 = 0.084 2023 Q1 T1 1.009 2023 Applied Mathematics 2023 Q1 4.3 2023 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion López, José L. Pérez Sinusía, Ester Universidad de Zaragoza (orcid)0000-0002-8021-2745 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 150, 1 (2023), 254-275 Stud. appl. math. STUDIES IN APPLIED MATHEMATICS 0022-2526 1224102 http://zaguan.unizar.es/record/121184/files/texto_completo.pdf Versión publicada 1496305 http://zaguan.unizar.es/record/121184/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:121184 articulos driver 2024-11-22-11:57:50 ARTICLE