Bohr-Mollerup theorem

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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 $x$.


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