# Difference between revisions of "Bohr-Mollerup theorem"

From Encyclopedia of Mathematics

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− | The [[Gamma-function|gamma-function]] on the positive real axis is the unique positive, logarithmically convex function | + | 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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<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.P. Boas, "Bohr's power series theorem in several variables" ''Proc. Amer. Math. Soc.'' , '''125''' (1997) pp. 2975–2979</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> C. Caratheodory, "Theory of functions of a complex variable" , '''1''' , Chelsea (1983) pp. Sects. 274–275</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> H.P. Boas, "Bohr's power series theorem in several variables" ''Proc. Amer. Math. Soc.'' , '''125''' (1997) pp. 2975–2979</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top"> C. Caratheodory, "Theory of functions of a complex variable" , '''1''' , Chelsea (1983) pp. Sects. 274–275</TD></TR></table> |

## Revision as of 20:46, 27 April 2012

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

[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: http://encyclopediaofmath.org/index.php?title=Bohr-Mollerup_theorem&oldid=25621

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