Research

Google Scholar page.

 

Book: Lattice Sums Then and Now

monograph on chemical lattice sums, coauthored with J. M. Borwein, M. L. Glasser, R. C. McPhedran and I. J. Zucker, published by Cambridge University Press.

 


 

Some papers:

Random walks:

  • Some arithmetic properties of short random walk integrals, (with J. M. Borwein, D. Nuyens and A. Straub), Ramanujan Journal 26 (2011), 109-132 (PDF)
  • Three-step and four-step random walk integrals, (with J. M. Borwein and A. Straub), Experimental Mathematics 22 (2013), 1-14 (PDF)
  • Densities of short uniform random walks, (with J. M. Borwein, A. Straub, W. Zudilin and an appendix by D. Zagier), Canadian Journal of Mathematics 64 (2012), 961-990 (PDF)

Series for 1/pi:

  • Holonomic alchemy and series for 1/pi, (with S. Cooper and W. Zudilin), Alladi60 (2017), 179-205 (PDF)
  • Legendre polynomials and Ramanujan-type series for 1/pi, (with H. H. Chan and W. Zudilin), Israel Journal of Mathematics 194 (2013), 183-207 (PDF)
  • Generating functions of Legendre polynomials: a tribute to Fred Brafman, (with W. Zudilin), Journal of Approximation Theory 164 (2012), 488-503 (PDF)
  • Complex series for 1/pi, (with H. H. Chan and W. Zudilin), Ramanujan Journal 29 (2012), 135-144 (PDF)
  • Series for 1/pi Using Legendre’s Relation, Integral Transforms and Special Functions 25 (2014), 1-14 (PDF)
  • Hypergeometric generating functions and series for 1/pi, Communications in Computer Algebra 47 (2013), 114-115

Elliptic integrals:

  • Moments of Ramanujan’s generalized elliptic integrals and extensions of Catalan’s constant, (with D. Borwein, J. M. Borwein and M. L. Glasser), Journal of Mathematical Analysis and Applications 384 (2011), 478-496
  • Log-sine evaluations of Mahler measures II, (with D. Borwein, J. M. Borwein and A. Straub), Integers 12A (2012), #A5 (PDF)
  • Moments of products of elliptic integrals, Advances in Applied Mathematics 48 (2012), 121-141 (PDF)
  • Moments of elliptic integrals and critical L-values, (with M. Rogers and I. J. Zucker), Ramanujan Journal 37 (2015), 113-130 (PDF)
  • Integrals of K and E from lattice sums, (with I. J. Zucker), Ramanujan Journal 40 (2016), 257-278 (PDF)

Double sums:

  • Some notes on weighted sum formulae for double zeta values, Number Theory and Related Fields, Springer Proceedings in Mathematics & Statistics 43 (2013), 361-379 (PDF)
  • Some double sums involving ratios of binomial coefficients arising from urn models, (with D. Stenlund), Journal of Integer Sequences 22 (2019), Article 19.1.8

Some presentations:

  • (2017) MATRIX workshop, Australia: Ramanujan-type series for 1/pi
  • (2016) INRIA, France: Some recent advances in Ramanujan-type series for 1/pi
  • (2015) OPSFA13, USA: Integrals involving powers of K
  • (2014) npqr2 international workshop: Some new series for 1/pi
  • (2013) SUTD: A case study in experimental mathematics (PDF)
  • (2013) NUS: Integrals involving products of elliptic integrals
  • (2013) ISSAC 2013, USA: Hypergeometric generating functions and series for 1/pi
  • (2013) Newcastle: Elliptic integrals, L-values and lattice sums
  • (2012) CARMA seminar: Elementary proofs for sums of double zeta values (PDF)
  • (2011) AustMs 11 (B. H. Neumann Prize): Legendre polynomials and pi (PDF)
  • (2011) AustMs 11: Logsin integrals and other topics in experimental mathematics (keynote on behalf of J. M. Borwein)
  • (2011) CARMA seminar: Legendre polynomials, modularity, and pi
  • (2010) AustMs 10: Densities of random walks (PDF)
  • (2010) Workshop on experimentation and computation in number theory: Number theoretical aspects of random walks (PDF)
  • (2010) CARMA seminar: Moments of products of elliptic integrals (PDF)
  • (2009) Newcastle: Random walk integrals (PDF)