10.46298/hrj.2021.7429
https://hrj.episciences.org/7429
Berndt, Bruce,
Bruce
Berndt
Dixit, Atul
Atul
Dixit
Ramanujan's Beautiful Integrals
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.
episciences.org
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]
2021-05-06
2021-05-06
2021-05-06
en
journal article
https://hal.archives-ouvertes.fr/hal-03208369v1
2804-7370
https://hrj.episciences.org/7429/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 43 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2020
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