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 *a*_{n} 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 Series: Examples, Alternate Form, Current Usage

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