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 $x$.
References
| [1] | E. Artin, "The gamma function", Holt, Rinehart & Winston (1964) |
| [2] | H.P. Boas, "Bohr's power series theorem in several variables" Proc. Amer. Math. Soc., 125 (1997) pp. 2975–2979 |
| [3] | C. Caratheodory, "Theory of functions of a complex variable", 1, Chelsea (1983) Sects. 274–275 |
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