Convergent and asymptotic expansions of the Pearcey integral
Ver/
Fecha
2015Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1016/j.jmaa.2015.04.078
Resumen
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 meth ...
[++]
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. [--]
Materias
Pearcey integral,
Third order differential equations,
Asymptotic expansions,
Green functions,
Fixed point theorems
Editor
Elsevier
Publicado en
Journal of Mathematical Analysis and Applications, 430 (2015) 181–192
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila
Versión del editor
Entidades Financiadoras
The Universidad Pública de Navarra is acknowledged by its financial support.