Papers*

  1. A q-analog of Euler's reduction formula for the double zeta function, (with Xia Zhou), Computational and Analytical Mathematics, Springer Proceedings in Mathematics & Statistics Vol. 50 in honor of Jonathan Borwein's 60th birthday, 2013, pp. 113--126.
    [PDF]

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  2. An infinite series for the natural logarithm that converges throughout its domain and makes concavity transparent, April 16, 2012.
    [PDF]

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  3. On Mordell-Tornheim sums and multiple zeta values, (with Xia Zhou) Annales des sciences mathématiques du Québec, Vol. 34, No. 1, 2010, pp. 15--23. [MR 2744193] (2011k:11118)
    [PDF]

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  4. Counting ordered pairs, Mathematics Magazine, Vol. 83, No. 4, October 2010, p. 302. DOI: 10.4169/002557010X528032
    [PDF]

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  5. Depth reduction of a class of Witten zeta functions, (with Xia Zhou and Tianxin Cai), Electronic Journal of Combinatorics, Vol. 16, No. 1, July 2009, #N27. [MR 2529818] (2010i:11137)
    [PDF] [PS]

    6.  
  6. A curious way to test for primes explained, Mathematics Magazine, Vol. 82, No. 3, June 2009, pp. 215--219.
    [PDF]

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  7. On shutting up and listening, MAA Focus, Vol. 29, No. 1, January 2009, pp. 20--21.
    [PDF]

    8.  
  8. Hypergeometric functions related to series acceleration formulas, pp. 113--125 in Tapas in Experimental Mathematics, Proceedings of the AMS Special Session on Experimental Mathematics held January 5, 2007 in New Orleans, Louisiana. Tewodros Amdeberhan and Victor Moll eds., Contemporary Mathematics, Vol. 457, American Mathematical Society, Providence, Rhode Island, 2008. ISBN: 978-0-8218-4317-8. [MR 2427667] (2009i:11101)

    9.  
  9. A signed analog of Euler's reduction formula for the double zeta function, June 26, 2007.
    [DVI] [PS] [PDF]

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  10. Signed q-analogs of Tornheim's double series, (with Xia Zhou and Tianxin Cai), Proceedings of the American Mathematical Society, Vol. 136, No. 8, August 2008, pp. 2689--2698. DOI: 10.1090/S0002-9939-08-09208-3 [MR 2399030] (2009b:11161)
    [DVI] [PS] [PDF] [Abstract, References and Article Information]

    11.  
  11. Thirty-two Goldbach variations, (with Jonathan M. Borwein), International Journal of Number Theory, Vol. 2, No. 1, 2006, 65--103. DOI: 10.1142/S1793042106000383 [MR 2217795] (2007e:11109)

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  12. Experimental determination of Apéry-like identities for ζ(2n+2), (with Jonathan M. Borwein and David H. Bailey), Experimental Mathematics, Vol. 15, No. 3, 2006, pp. 281--289. [MR 2264467] (2007f:11144)

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  13. Peg jumping for fun and profit (with Hugh Thomas), April 1, 2005.

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  14. Counting the positive rationals: a brief survey, August 29, 2005.

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  15. A q-analog of Euler's decomposition formula for the double zeta function, International Journal of Mathematics and Mathematical Sciences, Vol. 2005, Issue 21, 2005, pp. 3453--3458. DOI: 10.1155/IJMMS.2005.3453 [MR 2206867] (2006k:11174)
    Reprint: [PDF]

    16.  
  16. On the sum formula for multiple q-zeta values, Rocky Mountain Journal of Mathematics, Vol. 37, No. 5, 2007, pp. 1427--1434. [MR 2382894] (2009a:11188)
    [PDF]

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  17. Parametric Euler sum identities (with David Borwein and Jonathan M. Borwein), Journal of Mathematical Analysis and Applications, Vol. 316, Issue 1, April 2006, pp. 328--338. DOI: 10.1016/j.jmaa.2005.04.040 [MR 2201764] (2007b:11132)
    Reprint: [PDF]

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  18. An engaging puzzle to explore algebraic generalizations (co-authored with Tod Shockey), Mathematics Teacher, Vol. 99, No. 8, April 2006, pp. 532--536. National Council of Teachers of Mathematics.

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  19. Duality for finite multiple harmonic q-series, Discrete Mathematics, Vol. 300, Issues 1--3, pages 44--56. DOI: 10.1016/j.disc.2005.06.008 [MR 2170113] (2006m:05019)
    Galley: [PDF]

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  20. Multiple q-zeta values, Journal of Algebra, Vol. 283, Issue 2, 15 January 2005, pp. 752 -- 798. DOI: 10.1016/j.jalgebra.2004.09.017 [MR 2111222] (2006f:11106)
    Preprints: [DVI] [PS] Reprint: [PDF]

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  21. The distribution of the irreducibles in an algebraic number field (with Ali E. Özlük, Rebecca A. Rozario, and C. Snyder), Journal of the Australian Mathematical Society, Vol. 79, Part 3, December 2005, pp. 369--390. [MR 2190688] (2006g:11221)
    Preprints: [DVI] [PS] Reprint: [PDF]

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  22. Partition identities for the multiple zeta function, pages 19--29 in Zeta Functions, Topology, and Quantum Physics, Springer Series: Developments in Mathematics, Vol. 14, T. Aoki, S. Kanemitsu, M. Nakahara, Y. Ohno (eds.) 2005, XVI, 219 p. 13 illus., Hardcover ISBN: 978-0-387-24972-9. DOI: 10.1007/0-387-24918-8_2 [MR 2179270] (2006f:11105)
    [DVI] [PS] [PDF]

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  23. Resolution of some open problems concerning multiple zeta evaluations of arbitrary depth (with Douglas Bowman), Compositio Mathematica, October 2003, Vol. 139, Issue 1, pp. 85--100. DOI: 10.1023/B:COMP.0000005036.52387.da [MR 2024966] (2005f:11196)
    [DVI] [PS] [PDF]

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  24. A pair of difference differential equations of Euler-Cauchy type, Transactions of the American Mathematical Society, Vol. 355, No. 12, December 2003, pp. 4985--5002. [MR 1997592] (2004g:34119)
    Reprints: [DVI] [PS] [PDF]

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  25. A remark on Cavalieri's quadrature formula, The American Mathematical Monthly, Vol. 110, No. 5, May 2003, p. 437.
    [DVI] [PS] [PDF]

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  26. Representing the mean residual life in terms of the failure rate (co-authored with Ramesh C. Gupta), Mathematical and Computer Modelling, Vol. 37, No. 12--13, 2003, pp. 1271--1280. [MR 1996036] (2004e:62181)
    Preprints: [DVI] [PS] Reprint: [PDF]

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  27. Some remarks on sinc integrals and their connection with combinatorics, geometry and probability, Analysis (Munich), Vol. 22, No. 2, 2002, pp. 219--224. [MR 1916426] (2003i:42012)
    [DVI] [PS] [PDF]

    28.  
  28. On a class number formula for real quadratic fields (co-authored with Ali E. Özlük and C. Snyder), Bulletin of the Australian Mathematical Society, Vol. 65, No. 2, 2002, pp. 259--270. [MR 1898540] (2003a:11112)
    [DVI] [PS] [PDF]

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  29. Some multi-set inclusions associated with shuffle convolutions and multiple zeta values (co-authored with Douglas Bowman and Ji Hoon Ryoo), European Journal of Combinatorics, Vol. 24, No. 1, 2003, pp. 121--127. [MR 1957970] (2004c:11115)
    [DVI] [PS] [PDF]

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  30. Series acceleration formulas for Dirichlet series with periodic coefficients, The Ramanujan Journal, Vol. 6, No. 3, September 2002, pp. 331--346. DOI: http://dx.doi.org/10.1023/A:1019701516191 [MR 1926998] (2003g:11094)
    [DVI] [PS] [PDF] [Abstract]

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  31. Limiting behaviour of the mean residual life (co-authored with Ramesh C. Gupta), Annals of the Institute of Statistical Mathematics, Vol. 55, No. 1, March 2003, pp. 217--226. DOI: http://dx.doi.org/10.1007/BF02530495 [MR 1965973] (2004b:62215)
    [DVI] [PS] [PDF]

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  32. Multiple polylogarithms: A brief survey, (co-authored with Douglas Bowman), pages 71--92 in "Proceedings of a Conference on q-Series with Applications to Combinatorics, Number Theory and Physics," (Urbana, Illinois, 2000, Bruce C. Berndt and Ken Ono eds.) American Mathematical Society, Contemporary Mathematics, Vol. 291, Providence, Rhode Island, 2001. [MR 1874522] (2003c:33021)
    [DVI] [PS] [PDF]

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  33. The algebra and combinatorics of shuffles and multiple zeta values, (co-authored with Douglas Bowman), Journal of Combinatorial Theory, Series A, Vol. 97, No.1, 2002, pp. 43--61. DOI: 10.1006/jcta.2001.3194 [MR 1879045] (2003j:05010)
    Reprints: [DVI] [PS] [PDF]

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  34. On the distribution of the sum of n non-identically distributed uniform random variables, (co-authored with Ramesh C. Gupta), Annals of the Institute of Statistical Mathematics, Vol. 54, No. 3, 2002, pp. 689--700. DOI: 10.1023/A:1022483715767 [MR 1932412] (2003h:60029)
    [DVI] [PS] [PDF]

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  35. More Apéry-like formulae: On representing values of the Riemann zeta function by infinite series damped by central binomial coefficients, August 1, 2002.
    [DVI] [PS] [PDF]

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  36. Verhulst's logistic curve, The College Mathematics Journal, Vol. 32, No. 2, March 2001, pp. 94--98. [MR 1833354] (2002c:26002)
    Galley: [PDF] Preprints: [DVI] [PS] PDF]

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  37. Using integral transforms to estimate higher order derivatives, The American Mathematical Monthly, Vol. 107, No. 10, December 2000, pp. 923--931. [MR 1807002] (2001m:26002)
    [DVI] [PS] [PDF]

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  38. The harmonic series and the nth term test for divergence, The American Mathematical Monthly, Vol. 107, No. 7, August-Septemeber 2000, p. 651.
    [DVI] [PS] [PDF]

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  39. Computational strategies for the Riemann zeta function, (co-authored with Jonathan M. Borwein and Richard E. Crandall), Journal of Computational and Applied Mathematics, Vol. 121, No. 1-2, September 2000, pp. 247--296. DOI: MR 1780051] (2001h:11110)
    Preprint: [DVI] Reprints: [PS] [PDF]

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  40. Special values of multiple polylogarithms, (co-authored with Jonathan M. Borwein, David J. Broadhurst and Petr Lisonek), Transactions of the American Mathematical Society, Vol. 353, No. 3, March 2001, pp. 907--941. [MR 1 709772] (2003i:33003)
    [DVI] [PS] [PDF]

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  41. A class of series acceleration formulae for Catalan's constant, The Ramanujan Journal, Vol. 3, Issue 2, June 1999, pp. 159--173. DOI: 10.1023/A:1006945407723 [MR 1703281] (2000f:11163)
    [DVI] [PS] [PDF]

    42.  
  42. Combinatorial aspects of multiple zeta values, (co-authored with Jonathan M. Borwein, David J. Broadhurst and Petr Lisonek), The Electronic Journal of Combinatorics, Vol. 5, No. 1, 1998, #R38. [MR 1637378] (99g:11100)
    [DVI] [PS] [PDF]

    43.  
  43. Representations of Catalan's constant, (an unpublished catalog of formulae for the alternating sum of the reciprocals of the odd positive squares), 1998.

    44.  
  44. Empirically determined Apéry-like formulae for ζ(4n+3), (co-authored with Jonathan M. Borwein), Experimental Mathematics, Vol. 6, Issue 3, October 1997, pp. 181--194. [MR 1481588] (98m:11142)
    [DVI] [PS] [PDF]

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  45. A difference differential equation of Euler-Cauchy type, (co-authored with Harold G. Diamond), Journal of Differential Equations, Vol. 138, No. 2, August 10, 1997, pp. 267--300. [MR 1462269] (99a:34172)
    [DVI] [PS] [PDF]

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  46. Evaluations of k-fold Euler/Zagier sums: A compendium of results for arbitrary k, (co-authored with Jonathan M.Borwein and David J. Broadhurst), The Electronic Journal of Combinatorics, Vol. 4, No. 2, 1997, #R5, Wilf Festschrift. [MR 1444152] (98b:11091)
    [DVI] [PS] [PDF]

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  47. Ramanujan's formula for the logarithmic derivative of the gamma function, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 120, Part 3, October 1996, pp. 391--401. [MR 1388195] (97a:11132)
    [DVI] [PS] [PDF]

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  48. Searching symbolically for Apéry-like formulae for values of the Riemann zeta function, (co-authored with Jonathan M. Borwein), SIGSAM Bulletin of Symbolic and Algebraic Manipulation, Association of Computing Machinery, Vol. 30, No. 2, Issue 116, June 1996, pp. 2--7.
    [DVI] [PS] [PDF]

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  49. A sieve auxiliary function (from Ph.D. Thesis), pages 173--210 in "Analytic Number Theory: Proceedings of a Conference in Honor of Heini Halberstam," Vol. 1 (Allerton Park, Illinois, 1995, Bruce C. Berndt et al. eds.), Progress in Mathematics, Vol. 138, Birkhaüser, Boston, MA, 1996. [MR 1399338] (97h:11099)
    [DVI] [PS] [PDF]

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  50. On a claim of Ramanujan about certain hypergeometric series, Proceedings of the American Mathematical Society, Vol. 121, No. 4, August 1994, pp. 1145--1149. [MR 1189537] (94j:33003)
    [DVI] [PS] [PDF]
* Reviews of these articles in "Mathematical Reviews" can be accessed individually by clicking on the appropriate MR numbers. Of course, your machine must have the appropriate MathSciNet license. These reviews can be also be accessed ensemble from the Mathematical Reviews website.

The articles themselves can be obtained (in postcript format) by clicking on the respective titles. Links to coauthors and to the appropriate journal issues are provided when they exist.