English

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

R2 v1 2026-06-24T11:20:15.142Z