Möbius function
Multiplicative function in number theory / From Wikipedia, the free encyclopedia
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This article is about the number-theoretic Möbius function. For the combinatorial Möbius function, see incidence algebra. For the rational functions defined on the complex numbers, see Möbius transformation.
The Möbius function μ(n) is a multiplicative function in number theory introduced by the German mathematician August Ferdinand Möbius (also transliterated Moebius) in 1832.[lower-roman 1][lower-roman 2][2] It is ubiquitous in elementary and analytic number theory and most often appears as part of its namesake the Möbius inversion formula. Following work of Gian-Carlo Rota in the 1960s, generalizations of the Möbius function were introduced into combinatorics, and are similarly denoted μ(x).
Quick Facts Named after, Publication year ...
Named after | August Ferdinand Möbius |
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Publication year | 1832 |
Author of publication | August Ferdinand Möbius |
No. of known terms | infinite |
First terms | 1, −1, −1, 0, −1, 1, −1, 0, 0, 1 |
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