Series Relations
Two Dirichlet series involving the divisor function are:
which for d(n) = σ0(n) gives
and
A Lambert series involving the divisor function is:
for arbitrary complex |q| ≤ 1 and a. This summation also appears as the Fourier series of the Eisenstein series and the invariants of the Weierstrass elliptic functions.
Read more about this topic: Divisor Function
Famous quotes containing the words series and/or relations:
“Every day the fat woman dies a series of small deaths.”
—Shelley Bovey, U.S. author. Being Fat Is Not a Sin, ch. 1 (1989)
“She has problems with separation; he has trouble with unity—problems that make themselves felt in our relationships with our children just as they do in our relations with each other. She pulls for connection; he pushes for separateness. She tends to feel shut out; he tends to feel overwhelmed and intruded upon. It’s one of the reasons why she turns so eagerly to children—especially when they’re very young.”
—Lillian Breslow Rubin (20th century)