# Bohr-Mollerup theorem

From Encyclopedia of Mathematics

The gamma-function on the positive real axis is the unique positive, logarithmically convex function $f$ such that $f(1)=1$ and $f(x+1) = xf(x)$ for all $x$.

#### References

[a1] | H.P. Boas, "Bohr's power series theorem in several variables" Proc. Amer. Math. Soc. , 125 (1997) pp. 2975–2979 |

[a2] | C. Caratheodory, "Theory of functions of a complex variable" , 1 , Chelsea (1983) pp. Sects. 274–275 |

**How to Cite This Entry:**

Bohr-Mollerup theorem.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Bohr-Mollerup_theorem&oldid=25621

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