Ramanujan's Beautiful Integrals
Abstract
Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the \emph{Journal of the Indian Mathematical Society}, notebooks, Quarterly Reports to the University of Madras, letters to Hardy, published papers and the Lost Notebook. His evaluations are often surprising, beautiful, elegant, and useful in other mathematical contexts. He also discovered general methods for evaluating and approximating integrals. A survey of Ramanujan's contributions to the evaluation of integrals is given, with examples provided from each of the above-mentioned sources.
Keywords
Cite
@article{arxiv.2103.14002,
title = {Ramanujan's Beautiful Integrals},
author = {Bruce C. Berndt and Atul Dixit},
journal= {arXiv preprint arXiv:2103.14002},
year = {2021}
}
Comments
14 pages, to appear in the first special volume of the Hardy-Ramanujan Journal dedicated to the memory of Srinivasa Ramanujan