Hurwitz Zeta Function - Relation To Bernoulli Polynomials

Relation To Bernoulli Polynomials

The function defined above generalizes the Bernoulli polynomials:

where denotes the real part of z. Alternately,

In particular, the relation holds for and one has

Read more about this topic:  Hurwitz Zeta Function

Famous quotes containing the words relation to and/or relation:

    “Any relation to the land, the habit of tilling it, or mining it, or even hunting on it, generates the feeling of patriotism. He who keeps shop on it, or he who merely uses it as a support to his desk and ledger, or to his manufactory, values it less.”
    —Ralph Waldo Emerson (1803–1882)

    “There is the falsely mystical view of art that assumes a kind of supernatural inspiration, a possession by universal forces unrelated to questions of power and privilege or the artist’s relation to bread and blood. In this view, the channel of art can only become clogged and misdirected by the artist’s concern with merely temporary and local disturbances. The song is higher than the struggle.”
    —Adrienne Rich (b. 1929)