Dirichlet Series

(redirected from Abscissa of convergence)

Dirichlet series

[‚dē·rē′klā ‚sir·ēz]
(mathematics)
A series whose n th term is a complex number divided by n to the z th power.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Dirichlet Series

 

(named for P. G. L. Dirichlet), series of the form

where the an are constants and s = σ + it is a complex variable. For example, the series

represents the zeta function for σ > 1. The theory of Dirichlet series originally arose under the strong influence of analytic number theory. Eventually it developed into an extensive branch in the theory of analytic functions.

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.
References in periodicals archive ?
ON ENTRY, SIGMA0 CONTAINS THE VALUE C OF THE ABSCISSA OF CONVERGENCE OF C THE LAPLACE TRANSFORM FUNCTION TO BE C INVERTED OR AN UPPER BOUND TO THIS.