Dirichlet Series - Relation To Power Series

Relation To Power Series

The sequence an generated by a Dirichlet series generating function corresponding to:

where ζ(s) is the Riemann zeta function, has the ordinary generating function:

Read more about this topic:  Dirichlet Series

Famous quotes containing the words relation to, relation, power and/or series:

    Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking, love has found. Man judges of nature in relation to itself; the angelic spirit judges of it in relation to heaven. In short to the spirits everything speaks.
    Honoré De Balzac (1799–1850)

    The instincts of the ant are very unimportant, considered as the ant’s; but the moment a ray of relation is seen to extend from it to man, and the little drudge is seen to be a monitor, a little body with a mighty heart, then all its habits, even that said to be recently observed, that it never sleeps, become sublime.
    Ralph Waldo Emerson (1803–1882)

    [The Republican Party] consists of those who, believing in the doctrine that mankind are capable of governing themselves and hating hereditary power as an insult to the reason and an outrage to the rights of men, are naturally offended at every public measure that does not appeal to the understanding and to the general interest of the community.
    James Madison (1751–1836)

    Mortality: not acquittal but a series of postponements is what we hope for.
    Mason Cooley (b. 1927)