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.

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.

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.
0 NMAX = 550',/) 9090 FORMAT(//,2X, + THE EXAMPLE TEST IS'/ + F(Z) =1/ (Z*Z+Z+1) '// + WITH ITS INVERSE '/ +' F(T) = 2/SQRT(3) * EXP(-T/2)* SIN(T*SQRT(3)/2)'/// +//, 1X, A78) 9100 FORMAT (/,1X, 'ERROR DETECTED, I = ', I3, ' IFAIL =',100I3) 9110 FORMAT (/,' ABSCISSA OF CONVERGENCE > ',F5.