In mathematics, a Lambert series, named for Johann Heinrich Lambert, is a series taking the form
It can be resummed formally by expanding the denominator:
where the coefficients of the new series are given by the Dirichlet convolution of an with the constant function 1(n) = 1:
This series may be inverted by means of the Möbius inversion formula, and is an example of a Möbius transform.
Other articles related to "lambert series":
... The Lambert series of a sequence an is Note that in a Lambert series the index n starts at 1, not at 0 ...
... In the literature we find Lambert series applied to a wide variety of sums ... polylogarithm function, we may refer to any sum of the form as a Lambert series, assuming that the parameters are suitably restricted ... Thus which holds for all complex q not on the unit circle, would be considered a Lambert series identity ...
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