000121184 001__ 121184
000121184 005__ 20241125101126.0
000121184 0247_ $$2doi$$a10.1111/sapm.12539
000121184 0248_ $$2sideral$$a131696
000121184 037__ $$aART-2023-131696
000121184 041__ $$aeng
000121184 100__ $$0(orcid)0000-0002-3698-6719$$aFerreira, Chelo$$uUniversidad de Zaragoza
000121184 245__ $$aAsymptotic approximation of a highly oscillatory integral with application to the canonical catastrophe integrals
000121184 260__ $$c2023
000121184 5060_ $$aAccess copy available to the general public$$fUnrestricted
000121184 5203_ $$aWe 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.
000121184 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000121184 590__ $$a2.6$$b2023
000121184 592__ $$a1.009$$b2023
000121184 591__ $$aMATHEMATICS, APPLIED$$b28 / 332 = 0.084$$c2023$$dQ1$$eT1
000121184 593__ $$aApplied Mathematics$$c2023$$dQ1
000121184 594__ $$a4.3$$b2023
000121184 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion
000121184 700__ $$aLópez, José L.
000121184 700__ $$0(orcid)0000-0002-8021-2745$$aPérez Sinusía, Ester$$uUniversidad de Zaragoza
000121184 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000121184 773__ $$g150, 1 (2023), 254-275$$pStud. appl. math.$$tSTUDIES IN APPLIED MATHEMATICS$$x0022-2526
000121184 8564_ $$s1224102$$uhttps://zaguan.unizar.es/record/121184/files/texto_completo.pdf$$yVersión publicada
000121184 8564_ $$s1496305$$uhttps://zaguan.unizar.es/record/121184/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada
000121184 909CO $$ooai:zaguan.unizar.es:121184$$particulos$$pdriver
000121184 951__ $$a2024-11-22-11:57:50
000121184 980__ $$aARTICLE