Mathematica Eterna

Mathematica Eterna
Open Access

ISSN: 1314-3344


The Stokes phenomenon and the Lerch zeta function

R. B. Paris

We examine the exponentially improved asymptotic expansion of the Lerch zeta function L(λ, a, s) = P∞ n=0 exp(2πniλ)/(n + a) s for large complex values of a, with λ and s regarded as parameters. It is shown that an infinite number of subdominant exponential terms switch on across the Stokes lines arg a = ± 1 2 π. In addition, it is found that the transition across the upper and lower imaginary a-axes is associated, in general, with unequal scales. Numerical calculations are presented to confirm the theoretical predictions.