**CV**(click to download).

**Papers (Math)**

- A weighted extension of Fibonacci numbers, (with Archana Kumari and Michael Schlosser), preprint, 14pp.
- An uncountable number of proofs of the Pythagoras theorem (with Sagar Shrivastava), preprint, 9pp.
- Ramanujan's $q$-continued fractions, preprint, 15pp.
- Ramanujan and Heine's method, Encyclopedia of Srinivasa Ramanujan and his Mathematics, preprint, 6 pp. (to appear)
- Glaisher's divisors and infinite products (with Hartosh Singh Bal), Preprint, 17 pp. (Replaces and updates an earlier preprint.)
- Ramanujan and hypergeometric series, Encyclopedia of Srinivasa Ramanujan and his Mathematics, preprint, 6 pp. (to appear)
- Telescoping continued fractions for the error terms in Stirling's formula (with Krishnan Rajkumar), Preprint, 23 pp.
- Stanley-Elder-Fine theorems for colored partitions (with Hartosh Singh Bal), Math. Student (to appear), 15pp
- Ramanujan's general $q$-continued fractions, Encyclopedia of Srinivasa Ramanujan and his Mathematics, Preprint, 6 pp. (to appear)
- Orthogonal polynomials associated with a continued fraction of Hirschhorn (with Mourad E. H. Ismail), Ramanujan J. (to appear), 22 pp.
- The Partition-Frequency generation matrix (with Hartosh Singh Bal), Ramanujan J.,
**59**(2022), 51-86. - Expansion formulas for multiple basic hypergeometric series (with Surbhi Rai), Adv. Appl. Math,
**137**(2022), Paper 102329, 29 pp. - On Entry II.16.12: A continued fraction of Ramanujan (with Mourad E. H. Ismail), Int. J. Number Theory,
**17**(2021), 251-266 - Prime number conjectures from the Shapiro class structure (with Hartosh Singh Bal), INTEGERS,
**20**, #A11, (2020), 23 pp. - A partial theta function Borwein conjecture (with Michael Schlosser), Annals of Combinatorics,
**23**, (2019), 561-572 - Heine's method and $A_n$ to $A_m$ transformation formulas, Ramanujan J.,
**48**, (2019), 191-215. Reprint. - The determinant of an elliptic Sylvesteresque matrix (with Christian Krattenthaler), SIGMA,
**14**(2018), 052, 15pp. - Elliptic well-poised Bailey transforms and lemmas on root systems (with Michael Schlosser), SIGMA,
**14**(2018), 025, 44pp. - 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. - Spiral determinants (with Christian Krattenthaler), Linear Algebra Appl.,
**529**, 374-390 (2017) preprint. - Analogues of a Fibonacci-Lucas identity, Fibonacci Quart.,
**54 (no. 2)**,**,**(2016) preprint - 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) - In Praise of an Elementary Identity of Euler, Electronic J. Combinatorics,
**18 (2)**, 44pp, (2011). - D_n Basic Hypergeometric Series, The Ramanujan Journal,
**3**, 175-203 (1999). - A short proof of an identity of Sylvester, Int. J. Math. Math. Sci.,
**22**, 431-435 (1999). - Cn and Dn very-well-poised 10phi9 transformations (with Michael Schlosser), Const. Approx.,
**14**, 531-567 (1998). - A multivariable view of one-variable q-series, in Special Functions and Differential Equations (Madras 1997), Proceedings of a workshop held at IMSc., Madras, India, January 13-24, 1997, Allied Publishers, New Delhi, 60-72 (1998).
- A characterization of Inverse Relations (with Stephen C. Milne), Selected papers in honor of Adriano Garsia (Taormina, 1994), Discrete Math.,
**193**, 235-245 (1998). (*Selected as one of the best papers written in 1998 in Discrete Math. and Discrete Applied Math, by the Editors of these journals.*) - Generalized Bibasic Hypergeometric Series and their U(n) extensions (with Stephen C. Milne), Adv. Math.,
**131**, 188-252 (1997).

**Math Articles**

- Thank you, Dick, Dick Askey Libor Amicorum (Sept 2019) (A friendship book containing tributes and messages for Richard ("Dick") Allen Askey), 4pp.
- How to discover the exponential function $e^x$, At Right Angles,
**6 (no. 3)**, 9-12, (Nov 2017) - Of Math and Art: Paradoxes (Part 2 of 2) (with Punya Mishra), At Right Angles,
**4 (no. 2)**, 9-14, (Jul 2015). - Of Math and Art: Paradoxes: True and/or False (Part 1 of 2) (with Punya Mishra), At Right Angles,
**4 (no. 1)**, 21-27, (Mar 2015). - Of Math and Art: Self-Similarity (with Punya Mishra), At Right Angles,
**3 (no. 2)**, 23-30, (Jul 2014). - How to discover 22/7 and other rational approximations to $\pi$, 5pp, At Right Angles,
**3 (no. 1)**, 49-53, (Mar 2014). At Right Angles,**Of Math and Art: Introducing Symmetry (with Punya Mishra),****3 (no. 1)**, 25-30, (Mar 2014).**Of Math and Art: Introducing Ambigrams (with Punya Mishra), At Right Angles, 2 (no. 3), 28-33 (Nov 2013).**

**Books**

- Get Smart! Maths Concepts, Penguin Books (Imprint: Puffin), India, 2008. Buy
- An Introduction to Multimedia Systems (co-edited with Sugata Mitra and Shikha Mehta), Academic Press, USA, 2002. Buy
- Inverse Relations, Generalized Bibasic Series, and their
*U(n)*extensions, Ph.D. Thesis, The Ohio State University, 1995. Download

**Other Publications (selected)**

- Technology in mathematics education (with Punya Mishra), Proceedings TIME 2007, IIT Bombay, (Dec 2007), 76-83.
**On the design of a learning environment, J.Sci. Ind. Res., 59 no. 8 & 9 701-709 (2000).****Performance based tests—A case study (with M. Kandan), in Cognitive Systems: Reviews and Previews, J. R. Isaac and K. Batra (eds.), Phoenix Publishing House, New Delhi; 793-805 (2000).****Minimal IT Literacy for UP School Principals, in Proceedings International Workshop on Advanced Learning Technologies (IWALT2000) Advanced Learning Technology: Design and Development Issues, New Zealand, IEEE Computer Society, December 2000.****Algorithms to Build a Better World, Book Review, J. Indian Education, May 2000.****On Automatically generating music (with Hem Bhatnagar), Proceedings of the F13 conference, NIIT Ltd., Nov 1998.****Mathematics Education in Primary Schools: A Snapshot (with A.K. Jalaluddin and Monika Kapoor), Proceedings of the F13 Conference, NIIT Ltd., Feb 1998.**