Bohr-Mollerup theorem

2020 Mathematics Subject Classification: Primary: 33B15 [MSN][ZBL]

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

[Ar]	E. Artin, "The gamma function", Holt, Rinehart & Winston (1964)
[Bo]	H.P. Boas, "Bohr's power series theorem in several variables" Proc. Amer. Math. Soc., 125 (1997) pp. 2975–2979
[Ca]	C. Caratheodory, "Theory of functions of a complex variable", 1, Chelsea (1983) Sects. 274–275