Ramanujan's approximation to the exponential function and generalizations
Number Theory
2022-05-18 v1 Combinatorics
Abstract
Ramanujan's approximation to the exponential function is reexamined with the help of Perron's saddle-point method. This allows for a wide generalization that includes the results of Buckholtz, and where all the asymptotic expansion coefficients may be given in closed form. Ramanujan's approximation to the exponential integral is treated similarly.
Keywords
Cite
@article{arxiv.2205.08504,
title = {Ramanujan's approximation to the exponential function and generalizations},
author = {Cormac O'Sullivan},
journal= {arXiv preprint arXiv:2205.08504},
year = {2022}
}
Comments
18 pages, 1 figure