# Euler constant

From Encyclopedia of Mathematics

The number defined by

considered by L. Euler (1740). Its existence follows from the fact that the sequence

is monotone increasing and bounded from above. The number-theoretic nature of the Euler constant has not been studied; it is not even known (1988) whether it is a rational number or not.

#### Comments

In fact, a relation

holds, cf. [a1], Chapt. 22.5.

#### References

[a1] | G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapts. 5; 7; 8 |

**How to Cite This Entry:**

Euler constant.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Euler_constant&oldid=17956

This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article