Lambert series

In mathematics, a Lambert series, named after Johann Heinrich Lambert, a series of the form

It can be umsummiert by extension to:

Where the coefficients of the new series by Dirichlet convolution of with the constant function 1 (n ) = 1 result:

Alternative form

Substituting, we obtain another common form of series:

In which

Is.

Examples of Lambert series in this form, with, occur in terms of the Riemann zeta function for odd natural numbers.

  • Sequences and series
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