International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 16, Pages 833-845
On defining the product
Department of Mathematics and Computer Science, Brandon University, Brandon R7A 6A9, Manitoba, Canada
Received 15 May 2003
Copyright © 2004 C. K. Li and V. Zou. 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.
Let be a fixed infinitely differentiable function defined on having the properties: (i) , (ii) for , and (iii) where and is the constant satisfying (iii). We overcome difficulties arising from computing 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 for and with the help of Pizetti's formula and the normalization.