International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 735-743

Regularization and asymptotic expansion of certain distributions defined by divergent series

Ricardo Estrada

Escuela de Mathemática, Universidad de Costa Rica, San José, Costa Rica

Received 4 May 1994; Revised 6 September 1994

Copyright © 1995 Ricardo Estrada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The regularization of the distribution n=δ(xpn). which gives a regularized value to the divergent series n=φ(pn) is obtained in several spaces of test functions. The asymptotic expansion as ϵ0+of series of the type n=0φ(ϵ pn) is also obtained.