ramanujan: Approximates the factorial :math:'n!' given an integer...

In aschleg/numberr: Numberr is a package containing number-theoretic algorithms and functions primarily written in C++ using Rcpp

Description

Ramanujan's formula is another factorial approximation method known for its accuracy in comparison to other factorial approximation approaches including Stirling's and Gosper's approximations. Ramanujan's formula is defined as:

n! \approx √{π} ≤ft(\frac{n}{e}\right)^n √[6]{8n^3 + 4n^2 + n + \frac{1}{30}}

Usage

ramanujan(n)

Arguments

n	integer to approximate factorial

Value

the approximated factorial, n!, as per Ramanujan's approximation.

References

Mortici, Cristinel. On Gosper's Formula for the Gamma Function. Valahia University of Targoviste, Department of Mathematics. Retrieved from http://files.ele-math.com/articles/jmi-05-53.pdf

Examples

ramanujan(10)
ramanujan(5)

aschleg/numberr documentation built on May 14, 2019, 10:31 a.m.