On some definite integrals connecting with certain infinite series
Ramesh Kumar Muthumalai
TL;DR
This paper explores definite integrals linked to infinite series, building on Ramanujan's work, and introduces recursive methods and generalizations for evaluating such integrals through infinite series.
Contribution
It presents new recursive techniques and generalizations for evaluating definite integrals connected to infinite series, extending Ramanujan's original results.
Findings
Recursive methods for integral evaluation
Generalizations of Ramanujan's integrals
New connections between integrals and infinite series
Abstract
We show some definite integrals connecting to infinite series, studied in Ramanujan's paper, titled "On question 330 of Professor Sanjana". We present few recursive methods to evaluate these definite integrals in various cases and we generalize this, to evaluate simliar kind of integrals through infinite series.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Mathematical Inequalities and Applications