Bruce Berndt ; Atul Dixit - Ramanujan's Beautiful Integrals

hrj:7429 - Hardy-Ramanujan Journal, May 6, 2021, Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - https://doi.org/10.46298/hrj.2021.7429
Ramanujan's Beautiful Integrals

Authors: Bruce Berndt ; Atul Dixit

Throughout his entire mathematical life, Ramanujan loved to evaluate definite integrals. One can find them in his problems submitted to the 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.


Volume: Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan
Published on: May 6, 2021
Submitted on: April 30, 2021
Keywords: modular equations,theta functions,lemniscate integral,beta and q-beta integrals,Riemann zeta function,Frullani's Theorem,Elliptic integrals,2010 Mathematics Subject Classification. 28-00, 33B99, 11M06,[MATH]Mathematics [math]


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