کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4614976 | 1339304 | 2015 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Convergent and asymptotic expansions of the Pearcey integral Convergent and asymptotic expansions of the Pearcey integral](/preview/png/4614976.png)
We consider the Pearcey integral P(x,y)P(x,y) for large values of |x||x|, x,y∈Cx,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 on analytic, in particular asymptotic, techniques applied to the integral definition of P(x,y)P(x,y). In this paper we consider a different method: the iterative technique used for differential equations in López, 2012. Using this technique in a differential equation satisfied by P(x,y)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|→∞|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.
Journal: Journal of Mathematical Analysis and Applications - Volume 430, Issue 1, 1 October 2015, Pages 181–192