Postprint version. Published in Bulgarian Journal of Physics, Volume 8, Issue 4, January 1, 1981, pages 313-328.
NOTE: At the time of publication, the author Todor D. Todorov was not yet affiliated with Cal Poly.
The class F of "quasi-extended asymptotic functions" introduced in the present paper contains all extended asymptotic functions [8, (3.1)] (in particular, all examples constructed in [9, Sec. 1 ]). But F contains also some new asymptotic functions very similar to tht Schwartz distributions. On the other hand, every two quasi-extended asymptotic functions can be multiplied as opposed to the Schwartz distributions; in particular, the square 948;2 of an asymptotic function 948; similar to Dirac's delta-function is constructed as an example. The connection with the asymptotic functions introduced in  and  is established.
1981 Heron Press Limited.