The asymptotics of a new exponential sum
The absolutely convergent exponential sum [formula missing] is studied for m→+∞ and fixed p when the parameter θ is allowed to become large such that θ/m remains finite. This situation corresponds, in general, to the trace in the complex plane of the partial sums of Sp(θ;m) consisting of a multiple spiral structure. Numerical results are presented to illustrate the accuracy of the expansion.
Paris, R. B. 2009. The asymptotics of a new exponential sum. Journal of Computational and Applied Mathematics. 223(1): pp.314-325. Available from: DOI: 10.1016/j.cam.2008.01.014