It is not difficult to see that the results obtained in (2.4) and (2.9) when letting q [right arrow] 1 tend to the same results for the factorial function (see [3]).

Mortici, A class of integral approximations for the factorial function, Computers and Mathematics with Applications., 59 (2010), 2053-2058.

In many cases we use the factorial function of smaller intervals to characterize the whole poset.

We call B(n) the factorial function or binomial factorial function of the poset P.

Observe that each iteration yields only partial information of the entire factorial function and, thus, each iteration gives more information about the symbol fact (the entire factorial function) than all preceding ones.

Of course, the mapping [[phi].sub.fact] has a unique fixed point, which provides the meaning of the denotational specification (1), and such a fixed point matches up with the entire factorial function fact.

It is called the Smarandache double factorial function Sdf(n).

[4] Zhu Minhui, On the mean value of the Smarandache double factorial function, Scientia Magna, 2(2006), No.

How would the Smarandache function behave if this variation of the

factorial function were used in place of the standard

factorial function?

Abstract The sum of factorials function, also known as the left

factorial function, is defined as !n = 0!

Abstract For any positive integer n, the Smarandache triple factorial function [d3.sub.f](n) is defined to be the smallest integer such that [d3.sub.f](n)!!!

According to [1], for any positive integer n, the Smarandache triple factorial function [d3.sub.f](n) is defined to be the smallest integer such that [d3.sub.f](n)!!!

Abstract For any positive integer n, let Sdf(n) denotes the Smarandance double factorial function, then Sdf(n) is defined as least positive integer m such that m!!

For any positive integer n, let Sdf(n) denotes the Smarandance double factorial function, then Sdf(n) defined the least positive integer n such that m!!

Abstract For any positive integer n, the Smarandache double

factorial function Sdf(n) is defined as the least positive integer m such that m!!