and find homework help for other Math questions at eNotes. The letters R,Q, N, Z are the names of the set of the numbers, that have specific. So the rule is: n! = n × (n −1)!. Which says. "the factorial of any number is that number times the factorial of (that number minus 1)". So 10! = 10 × 9!, and !. n -Dimensional · n Dimensions · Natural Domain · Natural Logarithm · Natural Numbers · Negative Direction · Negative Exponents · Negative Number. The hyperfactorial function can be generalized to complex numbers in a similar way as the factorial function. Let us write them out in full: In the same way that n! The factorial function is formally defined by the product. What's a Prime Number? Legendre's formula gives the multiplicity of the prime p occurring in the prime factorization of n! Euler also developed a convergent product approximation for the non-integer factorials, which can be seen to be equivalent to the formula for the Gamma function above:. Representation through the Gamma-function allows evaluation of factorial of complex argument. This page was last edited on 15 July , at Wolfram Alpha can calculate exact results for the ceiling function and floor function applied to the binary , natural and common logarithm of n! However, there exist complex functions that are probably simpler in the sense of analytic function theory and which interpolate the factorial values. It may seem funny that in this case multiplying no numbers together results in 1, but it helps simplify a lot of equations. The reciprocals of factorials produce a convergent series whose sum is Euler's number e:. One can define the k -th factorial, denoted by n! In fact, this is no longer a recurrence relation but a functional equation. Floating-point representation of an approximated result allows going a bit further, but this also remains quite limited by possible overflow. Like how much money you have The value of 0! Number A number represents the value or quantity of something Factorials have many applications in number theory. Since the factorial is extended by the Pi function, for every complex value z where it is defined, we can write:. This page may be out of date. Wikimedia Commons has media related to Factorial function.