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After some computation, I have obtained a function FactorialPower[1, n, -1]. Clearly, FactorialPower[1, n, -1] equals Factorial[n] for all integer values of n. Is there a way to get this clearer representation?

Surprisingly, FullSimplify[FactorialPower[1, n, -1]] returns ComplexInfinity while FullSimplify[Factorial[n]] returns n!.

The aforementioned function is one of the solutions of a recursive equation and it would be nice if I could print out just n! instead of FactorialPower[1, n, -1].

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Since you are interested in integer n, give that information to FullSimplify.

FullSimplify[FactorialPower[1, n, -1], Assumptions -> {n ∈ Integers, n >= 1}]

This reduces to n! as you expect. The problem arises because FactorialPower accepts other than integer input.

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  • $\begingroup$ Why is the assumption n >= 1 better than the assumption n >= 0? A call FactorialPower[1, 0, -1] yields 1, which equals 0!. On the other hand, calling FullSimplify[FactorialPower[1, n, -1], Assumptions -> {n ∈ Integers, n >= 0}], I get ComplexInfinity. $\endgroup$
    – Antoine
    Feb 2, 2015 at 9:44

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