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International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 16, Pages 833-845
http://dx.doi.org/10.1155/S0161171204305193

On defining the product rklδ

Department of Mathematics and Computer Science, Brandon University, Brandon, Manitoba, Canada R7A 6A9

Received 15 May 2003

Copyright © 2004 Hindawi Publishing Corporation. 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.

Abstract

Let ρ(s) be a fixed infinitely differentiable function defined on R+=[0,) having the properties: (i) ρ(s)0, (ii) ρ(s)=0 for s1, and (iii) Rmδn(x)dx=1 where δn(x)=cmnmρ(n2r2) and cm is the constant satisfying (iii). We overcome difficulties arising from computing lδn and express this regular sequence by two mutual recursions and use a Java swing program to evaluate corresponding coefficients. Hence, we are able to imply the distributional product rklδ for k=1,2, and l=0,1,2, with the help of Pizetti's formula and the normalization.