Rational Values
The Hurwitz zeta function occurs in a number of striking identities at rational values. In particular, values in terms of the Euler polynomials :
and
One also has
which holds for . Here, the and are defined by means of the Legendre chi function as
and
For integer values of ν, these may be expressed in terms of the Euler polynomials. These relations may be derived by employing the functional equation together with Hurwitz's formula, given above.
Read more about this topic: Hurwitz Zeta Function
Famous quotes containing the words rational and/or values:
“... how can a rational being be ennobled by any thing that is not obtained by its own exertions?”
—Mary Wollstonecraft (17591797)
“During our twenties...we act toward the new adulthood the way sociologists tell us new waves of immigrants acted on becoming Americans: we adopt the host cultures values in an exaggerated and rigid fashion until we can rethink them and make them our own. Our idea of what adults are and what were supposed to be is composed of outdated childhood concepts brought forward.”
—Roger Gould (20th century)