000151401 001__ 151401 000151401 005__ 20251017144630.0 000151401 0247_ $$2doi$$a10.1016/j.jat.2025.106150 000151401 0248_ $$2sideral$$a143120 000151401 037__ $$aART-2025-143120 000151401 041__ $$aeng 000151401 100__ $$0(orcid)0000-0002-3698-6719$$aFerreira, Chelo$$uUniversidad de Zaragoza 000151401 245__ $$aThe Pearcey integral in the highly oscillatory region II 000151401 260__ $$c2025 000151401 5203_ $$aWe consider the Pearcey integral for large values of and bounded values of . The standard saddle point analysis is difficult to apply because the Pearcey integral is highly oscillating in this region. To overcome this problem we use the modified saddle point method introduced in López et al. (2009). A complete asymptotic analysis is possible with this method, and we derive a complete asymptotic expansion of for large , accompanied by the exact location of the Stokes lines. There are two Stokes lines that divide the complex plane in two different sectors in which behaves differently when is large. The asymptotic approximation is the sum of two asymptotic series whose terms are elementary functions of and . Both of them are of Poincaré type; one of them is given in terms of inverse powers of ; the other one in terms of inverse powers of , and it is multiplied by an exponential factor that behaves differently in the two mentioned sectors. Some numerical experiments illustrate the accuracy of the approximation. 000151401 536__ $$9info:eu-repo/grantAgreement/ES/MCINN/PID2022-136441NB-I00 000151401 540__ $$9info:eu-repo/semantics/closedAccess$$aby-nc-nd$$uhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.es 000151401 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000151401 700__ $$aLópez, José L. 000151401 700__ $$0(orcid)0000-0002-8021-2745$$aPérez Sinusía, Ester$$uUniversidad de Zaragoza 000151401 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000151401 773__ $$g309 (2025), 106150 [13 pp.]$$pJ. approx. theory$$tJournal of Approximation Theory$$x0021-9045 000151401 8564_ $$s581675$$uhttps://zaguan.unizar.es/record/151401/files/texto_completo.pdf$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2026-03-03 000151401 8564_ $$s1889529$$uhttps://zaguan.unizar.es/record/151401/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint$$zinfo:eu-repo/date/embargoEnd/2026-03-03 000151401 909CO $$ooai:zaguan.unizar.es:151401$$particulos$$pdriver 000151401 951__ $$a2025-10-17-14:26:02 000151401 980__ $$aARTICLE