Difference between revisions of "Bohr-Mollerup theorem"
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The [[Gamma-function|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 $x$. | The [[Gamma-function|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 $x$. | ||
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====References==== | ====References==== | ||
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+ | |valign="top"|{{Ref|Ar}}||valign="top"| E. Artin, "The gamma function", Holt, Rinehart & Winston (1964) | ||
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+ | |valign="top"|{{Ref|Bo}}||valign="top"| H.P. Boas, "Bohr's power series theorem in several variables" ''Proc. Amer. Math. Soc.'', '''125''' (1997) pp. 2975–2979 | ||
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+ | |valign="top"|{{Ref|Ca}}||valign="top"| C. Caratheodory, "Theory of functions of a complex variable", '''1''', Chelsea (1983) pp. Sects. 274–275 | ||
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+ | |} |
Revision as of 22:51, 27 April 2012
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) pp. Sects. 274–275 |
How to Cite This Entry:
Bohr-Mollerup theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bohr-Mollerup_theorem&oldid=25622
Bohr-Mollerup theorem. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Bohr-Mollerup_theorem&oldid=25622
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article