James Mc Laughlin
Assistant Professor
Department of Mathematics
West Chester University

Office: Room 179, 25 University Avenue Phone: 610-430-4417 Fax: 610-738-0578 Email: jmclaughl@wcupa.edu Webpage:   jmclaughlin

Address:
Department of Mathematics
Room 101, 25 University Avenue
West Chester University
West Chester, PA 19383
FAX: 610-738-0578

My Curriculum Vitae: DVI PS PDF

 Nancy Wyshinski and I are organizing a special session on continued fractions at the 2009 Joint Meetings in Washington, D.C.
Follow this link for information on submitting an abstract and other related matters, if you are interested in giving a talk in this special session.

 Nancy and I also organized special sessions on continued fractions at the 2006 Joint Meetings in San Antonio and 2004 Joint Meetings in Phoenix.
Click here for a page with pictures from the special session in San Antonio, and abstracts of the talks.
Click here for the schedule of the Phoenix special session.

Research Interests

My main areas of interest are in Number Theory.

I am currently working on various problems related to continued fractions.

Some of this work concerns the problem of finding polynomial solutions to Pell's equation (thereby being able to write down expressions for the fundamental unit in infinite families of real quadratic fields).

I have also investigated various convergence problems for q-continued fractions, and I and my thesis adviser, Douglas Bowman, recently partially settled a long-standing open problem on the convergence of the Rogers-Ramanujan continued fraction on the unit circle.

I am also interested in the problem of finding the regular continued fraction expansion of a number expressed in some other form (for example, as an infinite series or infinite product) and finding numbers with predictable patterns in their regular continued fraction expansions.

Another area of interest is the evaluation of polynomial continued fractions.

I am also interested in various problems in the area of Diophantine equations.

My Research Statement: DVI PS PDF

Teaching

Students can access course information through Blackboard .

Publications/Preprints (Note that the preprint version of papers on this page will differ to some extent from the version which eventually appeared in print)

• [1] Polynomial Continued Fractions (With D. Bowman)
  - Acta Arith. 103 (2002), no. 4, 329--342. DVI PS PDF
• [2] On the Divergence of the Rogers-Ramanujan Continued Fraction on the Unit Circle (With D. Bowman)
  - The Transactions of the American Mathematical Society 356 (2004), no. 8, 3325--3347. DVI PS PDF
• [3] Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields
  - J. London Math. Soc. (2) 67 (2003), no. 1, 16--28. DVI PS PDF
• [4] Multi-variable Polynomial Solutions to Pell's Equation and Fundamental Units in Real Quadratic Fields
  - Pacific J. Math. 210 (2003), no. 2, 335--349. DVI PS PDF
• [5] On The Divergence in the General Sense of $q$-Continued Fractions on the Unit Circle (With D. Bowman)
  - Communications in the Analytic Theory of Continued Fractions 11(2003), 25--49. DVI PS PDF
• [6] A Theorem on Divergence in the General Sense for Continued Fractions (With D. Bowman)
  - The Journal of Computational and Applied Mathematics  172, (2004) no. 2, pp 363--373. DVI PS PDF
• [7] Real Numbers with Polynomial Continued Fraction Expansions (with Nancy Wyshinski)
  - Acta Arith. 116 (2005), no. 1, 63-79. DVI PS PDF
• [8] Combinatorial Identities Deriving from the n-th Power of a $2 \times 2$ Matrix
  - INTEGERS: The Electronic Journal of Combinatorial Number Theory 4 (2004), A19, 14 pp. . DVI PS PDF
• [9] A Convergence Theorem for Continued Fractions of the Form $K_{n=1}^{\infty}a_{n}/1$ (with Nancy Wyshinski)
  - The Journal of Computational and Applied Mathematics, Volume 179 , Issues 1--2, 1 July 2005, Pages 255-262, containing the proceedings from the Conference on Orthogonal Functions and Related Topics, Roros, Norway, August 2003 . DVI PS PDF
• [10] Ramanujan and the Regular Continued Fraction Expansion of Real Numbers (with Nancy Wyshinski)
  - The Mathematical Proceedings of the Cambridge Philosophical Society, Volume 138 - Issue 03 - May 2005, pp 367 - 381. DVI PS PDF
• [11] Powers of a matrix and combinatorial identities (with B. Sury)
  - INTEGERS: The Electronic Journal of Combinatorial Number Theory 5 (2005), A13, 9 pp. DVI PS PDF
• [12] The Convergence and Divergence of $q$-Continued Fractions outside the Unit Circle (With D. Bowman)
  - The Rocky Mountain Journal of Mathematics 36 (2006), no. 3, 799--809. DVI PS PDF
• [13] The Convergence behavior of $q$-Continued Fractions on the Unit Circle (With D. Bowman)
  - The Ramanujan Journal 12 (2006), no. 2, 185--195. DVI PS PDF
• [14] Ramanujan and Extensions and Contractions of Continued Fractions (with Nancy Wyshinski)
  - The Ramanujan Journal 14 (2007), no. 3, 389--404. DVI PS PDF
• [15] Further Combinatorial Identities Deriving from the n-th Power of a $2 \times 2$ Matrix (with Nancy Wyshinski)
  - Discrete Applied Mathematics 154 (2006), no. 8, 1301--1308. DVI PS PDF
• [16] Continued Fractions with Multiple Limits (With D. Bowman)
  - Advances In Mathematics Volume 210 (2007), no. 2, 578-606. DVI PS PDF
• [17] A $q$-continued fraction (with Doug Bowman and Nancy Wyshinski)
  - International Journal of Number Theory Volume 2 (2006), no. 4, 523-547. DVI PS PDF
• [18] Continued Fractions and Generalizations with Many Limits: A Survey. (with Doug Bowman)
  - In the Proceedings of the Conference on Diophantine Analysis and Related Fields, Keio University, Yokohama, JAPAN, 7-10 March, 2006 , published as Seminar on Mathematical Sciences, 35, Keio University, Department of Mathematics, Yokohama (2006), 19-38. DVI PS PDF
• [19] Some properties of the distribution of the numbers of points on elliptic curves over a finite prime field (with Saiying He)
  -  Bulletin of the Australian Mathematics Society  75 (2007), no. 1, 135--149.. DVI PS PDF
• [20] Some more Long Continued Fractions, I (with Peter Zimmer)
  - Acta Arith.127 (2007), no. 4, 365--389.  DVI PS PDF
• [21] Symmetry and specializability in the continued fraction expansions of some infinite products
  -  The Journal of Number Theory 127 (2007), no. 2, 184--219.   DVI PS PDF
• [22] Some Observations on Khovanskii's Matrix Methods for extracting Roots of Polynomials (with B. Sury)
  - INTEGERS: The Electronic Journal of Combinatorial Number Theory 7 (2007), A48, 12 pp. DVI PS PDF
• [23] Rogers-Ramanujan-Slater Type Identities (with Andrew Sills and Peter Zimmer)
  - Electronic Journal of Combinatorics 15 (2008) #DS15, 59 pp. DVI PS PDF
• [24] Ramanujan-Slater Type Identities Related to the Moduli 18 and 24 (with Andrew Sills)
  - The Journal of Mathematical Analysis and Applications 344/2 (2008) 765-777. DVI PS PDF
• [25] Some identities between basic hypergeometric series deriving from a new Bailey-type transformation (with Peter Zimmer)
   - The Journal of Mathematical Analysis and Applications , 345/2 (2008) 670-677. DVI PS PDF
• [26] Some more identities of the Rogers-Ramanujan type (with Douglas Bowman and Andrew Sills)
  -  The Ramanujan Journal   Volume 18, Issue 3 (2009), Page 307  DVI PS PDF
• [27] Some new Families of Tasoevian- and Hurwitzian Continued Fractions
  -  Acta Arith..  135 (2008), no. 3, 247--268.   DVI PS PDF
• [28] Some Implications of the WP-Bailey Tree (with Peter Zimmer)
  - Advances in Applied Mathematics Volume 43, Issue 2, August 2009, Pages 162-175 . DVI PS PDF
• [29] Combinatorics of Ramanujan-Slater Type Identities (with Andrew Sills)
  - to appear in INTEGERS: The Electronic Journal of Combinatorial Number Theory. DVI PS PDF
• [30] Rogers-Ramanujan Computer Searches (with Andrew Sills and Peter Zimmer)
  -  Journal of Symbolic Computation Volume 44, Issue 8, August 2009, Pages 1068-1078   DVI PS PDF
• [31] Lifting Bailey Pairs to WP-Bailey Pairs (with Andrew Sills and Peter Zimmer)
  - Discrete Mathematics 309 (2009), pp. 5077-5091 DVI PS PDF
• [32] An Identity Motivated by an Amazing Identity of Ramanujan
  - To appear in   The Fibonacci Quarterly . DVI PS PDF
• [33] General WP-Bailey Chains (with Peter Zimmer)
  - To appear in   The Ramanujan Journal . DVI PS PDF
• [34] Asymptotics and Sequential Closures of Continued Fractions and Generalizations (with Douglas Bowman)
  - submitted. DVI PS PDF
• [35] Some Applications of a Bailey-type Transformation (with Peter Zimmer)
  - Submitted DVI PS PDF
• [36] Some implications of Chu's $_{10}\psi_{10}$ extension of Bailey's $_{6}\psi_{6}$ summation formula (with Andrew Sills and Peter Zimmer) - submitted. DVI PS PDF
• [37] Some new Transformations for Bailey pairs and WP-Bailey Pairs - submitted. DVI PS PDF
• [38] Some Further Transformations for WP-Bailey Pairs - submitted. DVI PS PDF
• [39] New Summation Formulae for some $q$-products - submitted. DVI PS PDF

Mathematical Ancestry (with some links)

• Douglas Bowman (Thesis Adviser)
• Basil Gordon
• Tom M. Apostol
• Derrick Henry Lehmer
  Derrick Henry Lehmer Obituary (From the Number Theory Web, reproduced, with permission, from Acta Arithmetica 62 (1992) 207-213 )
• Jacob David Tamarkin
• Andrei Andreevich Markov
• Pafnuty Lvovich Chebyshev
• Nikolai Dmitrievich Brashman
• J. J. Von Littrov
  (If anyone knows of web pages about D. H. Lehmer, Jacob Tamarkin or J. J. Von Littrov, I would be very pleased to hear about them)

Math Links

• Page of Math Links