Lambert Series

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.

Read more about Lambert SeriesExamples, Alternate Form, Current Usage

Other articles related to "lambert series":

Generating Function - Definitions - 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 ...
Lambert Series - Current Usage
... 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 ...

Famous quotes containing the words series and/or lambert:

    Autobiography is only to be trusted when it reveals something disgraceful. A man who gives a good account of himself is probably lying, since any life when viewed from the inside is simply a series of defeats.
    George Orwell (1903–1950)

    Our duty now is to keep alive—to exist. What becomes of a nation if its citizens all die?
    Dudley Nichols, U.S. screenwriter. Jean Renoir. George Lambert (George Sanders)