In mathematics, the Hurwitz zeta function, named after Adolf Hurwitz, is one of the many zeta functions. It is formally defined for complex arguments s with Re(s) > 1 and q with Re(q) > 0 by
This series is absolutely convergent for the given values of s and q and can be extended to a meromorphic function defined for all s≠1. The Riemann zeta function is ζ(s,1).
Read more about Hurwitz Zeta Function: Analytic Continuation, Series Representation, Integral Representation, Hurwitz's Formula, Functional Equation, Taylor Series, Laurent Series, Fourier Transform, Relation To Bernoulli Polynomials, Relation To Jacobi Theta Function, Relation To Dirichlet L-functions, Zeros, Rational Values, Applications, Special Cases and Generalizations
Famous quotes containing the word function:
“If the children and youth of a nation are afforded opportunity to develop their capacities to the fullest, if they are given the knowledge to understand the world and the wisdom to change it, then the prospects for the future are bright. In contrast, a society which neglects its children, however well it may function in other respects, risks eventual disorganization and demise.”
—Urie Bronfenbrenner (b. 1917)