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:
“I thought I never wanted to be a father. A child seemed to be a series of limitations and responsibilities that offered no reward. But when I experienced the perfection of fatherhood, the rest of the world remade itself before my eyes.”
—Kent Nerburn (20th century)
“When one walks, one is brought into touch first of all with the essential relations between one’s physical powers and the character of the country; one is compelled to see it as its natives do. Then every man one meets is an individual. One is no longer regarded by the whole population as an unapproachable and uninteresting animal to be cheated and robbed.”
—Aleister Crowley (1875–1947)