Bohr-Mollerup theorem

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2010 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
How to Cite This Entry:
Bohr–Mollerup theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bohr%E2%80%93Mollerup_theorem&oldid=22156