It was his insight into algebraical formulae, transformation of infinite series, and so forth, that was most amazing. On this side most certainly I have never met his equal, and I can compare him only with Euler and Jacobi.
~Hardy (page XXXV, Collected papers of Srinivasa Ramanujan)

My research interests are in Special Functions, Combinatorics and Elementary Number Theory. In particular, I am interested in Basic Hypergeometric series and their extensions over root systems and to Elliptic Hypergeometric series, continued fractions and elliptic combinatorics.
In all of these, the common thread is Ramanujan. I was attracted to my thesis advisor Steve Milne because he spoke about his theorems extending Ramanujan’s work.
Click on the following to get various views of my research.
- Complete list of publications (with links to download)
- Some blog posts on my research projects.
- My page on Mathscinet
- My papers/preprints on ArXiv
- A post about my (unofficial) PhD students, Archna and Surbhi.
My collaborators
- Hartosh Singh Bal (Caravan Magazine)
- Tejasi Bhatnagar (Wisconsin)
- Mourad Ismail (see also here)
- Christian Krattenthaler (Vienna) (See also here)
- Archna Kumari (IIT, Delhi)
- Steve Milne (Ohio State)
- Punya Mishra (Arizona State)
- Sugata Mitra (NIIT and Newcastle)
- Surbhi Rai (IIT, Delhi)
- Krishnan Rajkumar (JNU)
- Michael Schlosser (Vienna) (see also here)
- Sagar Shrivastava (TIFR)
Expository work on Ramanujan’s mathematics

I have created a site called Ramanujan Explained. It contains lectures on Ramanujan’s identities. The lectures are at a undergraduate level — we cover topics which are usually not covered in undergraduate math courses. There are also lecture notes which are updated regularly. These include exercises, so you can learn the techniques for yourself. Enjoy!
Here are some articles and papers meant for general or research audiences which contain some element of Ramanujan’s identities.
- How to discover the Rogers-Ramanujan Identities, Resonance, 20 (no. 5), 416-430, (May 2015).
- How to prove Ramanujan’s q-Continued Fractions, in Contemporary Mathematics: Ramanujan 125, K. Alladi, F. Garvan, A. J. Yee (eds.) 627, 49-68 (2014) (preprint)
- Orthogonal polynomials associated with a continued fraction of Hirschhorn (with Mourad E. H. Ismail), Ramanujan J. 61, (2023), 487-514.
- On Entry II.16.12: A continued fraction of Ramanujan (with Mourad E. H. Ismail), Int. J. Number Theory, 17 (2021), 251-266
- A bibasic Heine transformation formula and Ramanujan’s $_2\phi_1$ transformations, in Analytic Number Theory, Modular Forms and q-Hypergeometric Series,
In honor of Krishna Alladi’s 60th Birthday, University of Florida, Gainesville, Mar 2016, G. E. Andrews and F. G. Garvan (eds.), 99-122 (2017) preprint. - Ramanujan’s general q-continued fractions, in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
- Ramanujan and hypergeometric series, in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
- Ramanujan and Heine’s method, in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
- Ramanujan’s q-continued fractions, Contemporary Math., Amer. Math. Soc., Providence, RI, 819 (2025) 199–219.
- The Partition-Frequency generation matrix (with Hartosh Singh Bal), Ramanujan J., 59 (2022), 51-86.