Ramanujan's Beautiful Integrals

zbMATH Open1477.33021arXiv2103.14002MaRDI QIDQ5011704

Atul Dixit, Bruce C. Berndt

Publication date: 27 August 2021

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.

Full work available at URL: https://arxiv.org/abs/2103.14002

zbMATH Keywords

Riemann zeta functiontheta functionselliptic integralsmodular equationslemniscate integralFrullani's theorembeta and \(q\)-beta integrals

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Elliptic functions and integrals (33E05)

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