Gaurav Bhatnagar

Gaurav Bhatnagar is a mathematician who communicates the beauty of mathematics, engineers rich mathematical experiences for his students, and subjects them to a never-ending stream of bad jokes.

List of publications

CV (click to download).

Books

  1. Experience Mathematics, Hem Aunty Publications, 2025. Download.
  2. Maths puzzles for smart kids (with Tejasi Bhatnagar), Hachette, India, 2023. More information. Buy at amazon.in. NEW!
  3. Get Smart! Maths Concepts, Penguin Books (Imprint: Puffin), India, 2008. Buy
  4. An Introduction to Multimedia Systems (co-edited with Sugata Mitra and Shikha Mehta), Academic Press, USA, 2002. Buy
  5. Inverse Relations, Generalized Bibasic Series, and their U(n) extensions, Ph.D. Thesis, The Ohio State  University, 1995. Download


Papers (Math)

  1. Ramanujan and Heine’s method, in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
  2. Ramanujan and hypergeometric series,  in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
  3. Ramanujan’s general q-continued fractions, in Ramanujan: His life, legacy and mathematical influence, 6 pp. (to appear)
  4. An easy proof of Ramanujan’s famous congruences $p(5m+4)\equiv 0 \equiv \tau(5m+5) \pmod 5$ (with Hartosh Singh Bal),
    Séminaire Lotharingien de Combinatoire, 93, Article B93a (2025) 4 pp.
  5. Expansion formulas for elliptic hypergeometric series (with Archna Kumari), Proc. Amer. Math. Soc. 153 (2025), 3099-3112.
  6. An esoteric identity with many parameters and other elliptic extensions of elementary identities (with Archna Kumari and Michael Schlosser), New Zealand J. Math. 56 (2025), 15-32.
  7. Ramanujan’s q-continued fractions, in Applications and q-extentions of hypergeometric functions, Contemporary Math., Amer. Math. Soc., Providence, RI, 819, 199-219.
  8. An uncountable number of proofs of the Pythagoras theorem (with Sagar Shrivastava), Math. Mag., 97 (2024), 536-544; (available online).
  9. A weighted extension of Fibonacci numbers (with Archna Kumari and Michael Schlosser), J. Difference Equ. Appl., 29, (2023) 733-747 (availaible online, 2023).
  10. Glaisher’s divisors and infinite products (with Hartosh Singh Bal), J. Integer Seq., 27, (2024) Article 24.1.6, 22 pp. (Replaces and updates an earlier preprint.)
  11. Telescoping continued fractions for the error terms in Stirling’s formula (with Krishnan Rajkumar), J. Approx. Theory, 293, (2023), Paper 105943, 12 pp.
  12. Stanley-Elder-Fine theorems for colored partitions (with Hartosh Singh Bal), Math. Student, 92 (Nos. 1-2),(2023), 111-125.
  13. Orthogonal polynomials associated with a continued fraction of Hirschhorn (with Mourad E. H. Ismail), Ramanujan J. 61, (2023), 487-514. 
  14. The Partition-Frequency generation matrix (with Hartosh Singh Bal), Ramanujan J., 59 (2022), 51-86. 
  15. Expansion formulas for multiple basic hypergeometric series (with Surbhi Rai), Adv. Appl. Math, 137 (2022), Paper 102329, 29 pp.
  16. On Entry II.16.12: A continued fraction of Ramanujan (with Mourad E. H. Ismail), Int. J. Number Theory, 17 (2021), 251-266
  17. Prime number conjectures from the Shapiro class structure (with Hartosh Singh Bal), INTEGERS, 20, #A11, (2020), 23 pp. 
  18. A partial theta function Borwein conjecture (with Michael Schlosser), Annals of Combinatorics, 23, (2019), 561-572 
  19. Heine’s method and $A_n$ to $A_m$ transformation formulas, Ramanujan J., 48, (2019), 191-215.  Reprint.
  20. The determinant of an elliptic Sylvesteresque matrix (with Christian Krattenthaler), SIGMA, 14 (2018), 052, 15pp.
  21. Elliptic well-poised Bailey transforms and lemmas on root systems (with Michael Schlosser), SIGMA, 14 (2018), 025, 44pp.
  22. 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.
  23. Spiral determinants (with Christian Krattenthaler), Linear Algebra Appl., 529, 374-390 (2017) preprint. 
  24. Analogues of a Fibonacci-Lucas identity, Fibonacci Quart., 54 (no. 2), 166-171,  (2016) preprint
  25. How to discover the Rogers-Ramanujan Identities, Resonance, 20 (no. 5), 416-430, (May 2015).
  26. 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)
  27. In Praise of an Elementary Identity of Euler, Electronic J. Combinatorics, 18 (2), 44pp, (2011).
  28. D_n Basic Hypergeometric Series, The Ramanujan Journal, 3, 175-203 (1999).
  29. A short proof of an identity of Sylvester, Int. J. Math. Math. Sci., 22, 431-435 (1999).
  30. Cn and Dn very-well-poised 10phi9 transformations (with Michael Schlosser), Const. Approx., 14, 531-567 (1998).
  31. 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).
  32. 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.)
  33. Generalized Bibasic Hypergeometric Series and their U(n) extensions (with Stephen C. Milne), Adv. Math., 131, 188-252 (1997).

Math Articles

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

Other Publications (selected)

  1. Technology in mathematics education (with Punya Mishra), Proceedings TIME 2007, IIT Bombay, (Dec 2007), 76-83.
  2. On the design of a learning environment, J.Sci. Ind. Res., 59 no. 8 & 9 701-709 (2000).
  3. 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).
  4. 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.
  5. Algorithms to Build a Better World, Book Review, J. Indian Education, May 2000. (One of the references is now here.)
  6. On Automatically generating music (with Hem Bhatnagar), Proceedings of the F13 conference, NIIT Ltd., Nov 1998. 
  7. Mathematics Education in Primary Schools: A Snapshot (with A.K. Jalaluddin and Monika Kapoor), Proceedings of the F13 Conference, NIIT Ltd., Feb 1998.