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