Euler constant

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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.


In fact, a relation

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


[a1] G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapts. 5; 7; 8
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Euler constant. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article