Convergent and asymptotic expansions of the Pearcey integral
We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techn...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2015 |
| País: | España |
| Institución: | Universidad Pública de Navarra |
| Repositorio: | Academica-e. Repositorio Institucional de la Universidad Pública de Navarra |
| OAI Identifier: | oai:academica-e.unavarra.es:2454/31768 |
| Acceso en línea: | https://hdl.handle.net/2454/31768 |
| Access Level: | acceso abierto |
| Palabra clave: | Pearcey integral Third order differential equations Asymptotic expansions Green functions Fixed point theorems |
| Sumario: | We consider the Pearcey integral P(x; y) for large values of |x|, x, y ∈ C. We can find in the literature several convergent or asymptotic expansions in terms of elementary and special functions, with different levels of complexity. Most of them are based in analytic, in particular asymptotic, techniques applied to the integral definition of P(x; y). In this paper we consider a different method: the iterative technique used for differential equations in [Lopez, 2012]. Using this technique in a differential equation satisfied by P(x; y) we obtain a new convergent expansion analytically simple that is valid for any complex x and y and has an asymptotic property when |x|→ ∞ uniformly for y in bounded sets. The accuracy of the approximation is illustrated with some numerical experiments and compared with other expansions given in the literature. |
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