In mathematics, Euler-Mascheroni constant is a number that appears in analysis and number theory. It first appeared in the work of Swiss mathematician Leonhard Euler in the early 18th century. It is usually represented with the Greek letter (gamma), although Euler used the letters C and O instead.
It is not known yet whether the number is irrational (that is, cannot be written as a fraction with an integer numerator and denominator) or transcendental (that is, cannot be the solution of a polynomial with integer coefficients). The numerical value of is about . Italian mathematician Lorenzo Mascheroni also worked with the number, and tried unsuccessfully to approximate the number to 32 decimal places, making mistakes on five digits.
For , this gives
Using properties of the digamma function, can also be written as a limit.
- Euler, Leonhard (1735). De Progressionibus harmonicus observationes (PDF). pp. 150–161.
- "Greek/Hebrew/Latin-based Symbols in Mathematics". Math Vault. 2020-03-20. Retrieved 2020-10-05.
- Weisstein, Eric W. "Euler-Mascheroni Constant". mathworld.wolfram.com. Retrieved 2020-10-05.
- "Euler-Mascheroni Constant | Brilliant Math & Science Wiki". brilliant.org. Retrieved 2020-10-05.
- Sandifer, Edward (October 2007). "How Euler Did It - Gamma the constant" (PDF). Retrieved 26 June 2017.
- "The Euler Constant" (PDF). April 14, 2004. Retrieved June 26, 2017.