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 Series: Examples, Alternate Form, Current Usage
Famous quotes containing the words lambert and/or series:
“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)
“I look on trade and every mechanical craft as education also. But let me discriminate what is precious herein. There is in each of these works an act of invention, an intellectual step, or short series of steps taken; that act or step is the spiritual act; all the rest is mere repetition of the same a thousand times.”
—Ralph Waldo Emerson (1803–1882)