Dirichlet series [‚dē·rē′klā ‚sir·ēz]
Dirichlet Series
(mathematics)
A series whosenth term is a complex number divided bynto thezth power.
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.
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