---
tag: 9AFZ46MBJ0
kind: concept
name: Bhargava factorial
aliases: [bhargava-factorial-function, bhargavas-factorial-function, generalised-factorial, generalized-factorial, manjul-bhargava-factorial]
sources:
  - wikipedia: en:48496573@r1374012685
    locator: Bhargava factorial
    note: adopted
    mention: wikipedia://en/48496573
    sections: [Summary]
same_as:
  wikidata: Q25304332
  wikipedia: Bhargava factorial
inventory: [15XZ2WEA4H]
---

## Summary

In mathematics, **Bhargava's factorial function**, or simply the **Bhargava factorial**, is a generalization of the [[factorial|0XWG0JGDFW]] function developed by Manjul Bhargava as part of his bachelor's thesis at Harvard University in 1996. Bhargava subsequently published a revised version in *The American Mathematical Monthly* in 2000. The Bhargava factorial has the property that many number-theoretic results involving the ordinary factorials remain true even when the factorials are replaced by the Bhargava factorials. Using an arbitrary [[infinite subset|01MKW4R283]] *S* of the set $\mathbb{Z}$ of integers, Bhargava associated a positive integer with every positive integer *k*, which he denoted by *k* !<sub>*S*</sub>, with the property that if one takes *S* = $\mathbb{Z}$ itself, then the integer associated with *k*, that is *k* !<sub>$\mathbb{Z}$</sub>, would turn out to be the ordinary factorial of *k*.