Lambert summation - Alchetron, The Free Social Encyclopedia

In mathematical analysis, Lambert summation is a summability method for a class of divergent series.

Definition

A series ∑ a n is Lambert summable to A, written ∑ a n = A ( L ) , if

lim r → 1 − ( 1 − r ) ∑ n = 1 ∞ n a n r n 1 − r n = A .

If a series is convergent to A then it is Lambert summable to A (an Abelian theorem).

∑ n = 1 ∞ μ ( n ) n = 0 ( L ) , where μ is the Möbius function. Hence if this series converges at all, it converges to zero.

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