mathematical analysis, Lambert summation is a summability method for a class of divergent series.
A series is "Lambert summable" to "A", written , if
If a series is convergent to "A" then it is Lambert summable to "A" (an
* , where μ is the
Möbius function. Hence if this series converges at all, it converges to zero.
Abelian and tauberian theorems
*cite book | author=Hugh L. Montgomery | authorlink=Hugh Montgomery (mathematician) | coauthors=Robert C. Vaughan | title=Multiplicative number theory I. Classical theory | series=Cambridge tracts in advanced mathematics | volume=97 | year=2007 | isbn=0-521-84903-9 | pages=159-160
*cite journal | author=Norbert Wiener | authorlink=Norbert Wiener | title=Tauberian theorems | journal=Ann. Of Math. | year=1932 | volume=33 | pages=1–100 | doi=10.2307/1968102
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