Publications
H. al Kafri, D.J. Jeffrey, R.M. Corless: Rapidly convergent integrals and function evaluation. Springer LNCS, MACIS 2017.
D.J. Jeffrey, N. Murdoch: Stirling numbers, Lambert W and the Gamma function. Springer LNCS. MACIS 2017.
S.X. Liang, Y. Gao, L. Zou, D.J. Jeffrey: Selection of bases in operational calculus and its applications. Numerical Mathematics: Theory, methods and applications. Accepted August 2017.
K.A. Folitse, D.J. Jeffrey, R.M. Corless: Properties and computation of the functional inverse of Gamma. SYNASC 2017.
N. Khattak, D.J. Jeffrey: Rational Orthonormal Matrices. SYNASC 2017.
W.L. Fan, D.J. Jeffrey, E. Postma: Computation of some integer sequences in Maple. CASC 2017. LNCS 10490, Springer 2017.
D.J. Jeffrey: Branch structure and implementation of Lambert W. Mathematics in Computer Science, Vol 11 (3-4), pp 341-350. DOI: 10.1007/s11786-017-0320-6.
L. Zou, S. Liang, Y. Li, D.J. Jeffrey: Analytic approximations to nonlinear boundary value problems modeling beam-type nano-electromechanical systems. Zeitschrift f. Naturforschung, Vol 72(3), pp 201-206, 2017.
S. Ilie, D.J. Jeffrey, R.M. Corless, X. Zhang: Computation of Stirling numbers and generalizations. SYNASC 2015 proceedings. pp 57--60, IEEE Computer Soc. 2015. Preprint
D.J. Jeffrey, G.A. Kalugin, N. Murdoch: Lagrange inversion and Lambert W. SYNASC 2015 proceedings. pp 42--46, IEEE Computer Soc. 2015. Preprint
D. McDonald, D. Ouellet, M. Tchepel, P. Wild, J. Provan, D.J. Jeffrey: Wood Mechanics: From Chips to Flocs to Fibres - part I. J-FOR: Journal of science & technology for forest products and processes. Vol 4(5), 23--30, 2014.
D. McDonald, D. Ouellet, M. Tchepel, P. Wild, J. Provan, D.J. Jeffrey: Wood Mechanics: From chips to flocs to fibres - part II. J-FOR- Journal of science and technology for forest products and processes. Vol 4(5), 31--37, 2014.
D.J. Jeffrey: Multivalued elementary functions in computer-algebra systems. Proceedings AISC 2014. Lecture Notes in Computer Science, Vol 8884. Ed. Aranda-Corral, GA, Calmet, J, Martin-Mateos,FJ. pp 157--167, Springer 2014. DOI: 10.1007/978-3-319-13770-4_14 Print ISBN: 978-3-319-13769-8 Online ISBN: 978-3-319-13770-4 Preprint
D.J. Jeffrey, J.E. Jankowski: Branch differences and Lambert W. Proceedings SYNASC 2014, IEEE computer society, pp 61--65. ISBN: 978-1-4799-8447-3. DOI: 10.1109/SYNASC.2014.16 Offprint
R.M. Corless, D.J. Jeffrey, F. Wang: The asymptotic analysis of some interpolated nonlinear recurrence relations. Proceedings ISSAC 2014, ACM press, pp 115--121, 2014. Offprint
D. Tsarapkina, D.J. Jeffrey: Exploring rounding errors in Matlab using extended precision. Procedia Computer Science, Vol 29, pp 1423-1432, 2014.
J. Middeke, A. Almohaimeed, D.J. Jeffrey: Common factors in fraction-free matrix reduction. Proceedings SYNASC 2013, IEEE computer society, IBSN 978-1-4799-3035-7, pp76--80, 2013.
Z.L. Krougly, D.J. Jeffrey, D. Tsarapkina: Software implementation of Numerical Algorithms in Arbirary Precision. Proceedings SYNASC 2013, IEEE computer Society, ISBN 978-1-4799-3035-7, p131--137, 2013.
R.M. Corless, J. Hu, D.J. Jeffrey: Some definite integrals containing the Tree-T function. Communications in Computer Algebra, Vol 48:2, 33--41, 2014. PDF
D.J. Jeffrey, R.M. Corless: Linear Algebra in Maple. CRC Handbook of Linear Algebra, 2nd Edition. Ed: L. Hogden. 2013 Proof copy
R.M. Corless, D.J. Jeffrey: The Lambert W function. Princeton Companion to Applied Mathematics, 2014. PDF proof
J. Hu, Y. Hou, A.D. Rich, D.J. Jeffrey: Indefinite integration as term rewriting: integrals containing tangent. Programming and Computer Software, Vol 39(2), 61--66, 2013. Original Translation
G.A. Kalugin, D.J. Jeffrey, R.M. Corless: Bernstein, Pick, Poisson and related integral expressions for Lambert W. Integral Transforms and Special Functions. Vol 23(11) pp 817--829, 2012. DOI:10.1080/10652469.2011.640327 PDF preprint
G.A. Kalugin, D.J. Jeffrey, R.M. Corless, P.B.Borwein: Stieltjes and other integral representations for functions of Lambert W. Integral Transforms. Spec. Functions. Vol 23(8) pp 581--593, 2012. DOI:10.1080/10652469.2011.613830 PDF preprint.
G.A. Kalugin, D.J. Jeffrey: Unimodal sequences show Lambert W is Bernstein. Comptes Rendus/Mathematical Reports, Vol 33(2) June 2011. arXiv:1011.5940v1
J. Tanguay, M. Gil, D.J. Jeffrey, S.R. Valluri: D-dimensional Bose gases and the Lambert W function. J. Math Phys. Vol 51, issue 12, 123303, 2010. doi:10.1063/1.3496906 .
S. Liang, D.J. Jeffrey: An analytical approach for solving nonlinear boundary value problems in finite domains. Numerical Algorithms. Vol 56, issue 1, January 2011, pp 93--106. PDF preprint.
E. Shemyakova, S.I. Khashin, D.J. Jeffrey: Computers and Mathematics with Applications, Vol 60, issue 5, September 2010, pp 1360--1363. doi:10.1016/j.camwa.2010.06.017
G.A. Kalugin, D.J. Jeffrey: Series transformations to improve and extend convergence. In: CASC 2010, LNCS 6244, pp 134--147, Springer 2010. PDF offprint
Piers W. Lawrence, R.M. Corless, D.J. Jeffrey: Algorithm 917: Complex double-precision evaluation of the Wright omega function. ACM TOMS. Vol 38(3) Article 20. DOI 10.1145/2168773.2168779. April 2012.
D.J. Jeffrey: LU factoring of non-invertible matrices. Communications in Computer Algebra, volume 44, no. 1 issue 171, pp 1--8, 2010. preprint in PDF
D.J. Jeffrey, A.D. Rich: Reducing expression size using rule-based integration. In: Intelligent Computer Mathematics. Ed: S.Autexier, J.Calmet, D. Delahaye, P.D.F.Ion, L.Rideau,R.Rioboo,A.P.Sexton. LNAI 6167, Springer, pp234--246, (2010) PDF preprint also you can visit the .
A.D. Rich, D.J. Jeffrey: Efficiency considerations for indefinite integration by transformation rules. Systems Theory and Scientific Computation (ISTASC'09), WSEAS Press 2009.
Z. Krougly, D.J. Jeffrey: Implementation and application of extended precision in Matlab. Proc. Applied Computing Conference ACC'09, Editors: Mastorakis et al. pp 103-108, WSEAS Press 2009.
D.J. Jeffrey: Getting from x to y without crashing. Int. J. Technology Mathematics Education. Vol 17(2), pp 87--92, (2010) PDF preprint
S. Liang, J. Gerhard, D.J. Jeffrey, G. Moroz: A package for solving parametric polynomial systems. ACM Communications in Computer Algebra. Vol 43(3), pp 61--72, 2009.
S. Liang, D.J. Jeffrey: Approximate solutions to a parameterized sixth order boundary value problem. Computers and Mathematics with Applications. Vol 59(1), pp247--253, (2010). PDF preprint
S.R. Valluri, M. Gil, D.J. Jeffrey, S. Basu: The LambertW function and Quantum statistics. J. Math. Phys. Vol 50, 102103, doi:10.1063/1.3230482 (2009)
S. Liang, D.J. Jeffrey: An efficient analytical approach for solving fourth order boundary value problems. Computer Physics Communications Vol 180, pp 2034-2040 (2009) PDF preprint
S. Liang, D.J.Jeffrey: New travelling wave solutions to modified CH and DP equations. Computer Physics Communications. Vol 180, pp 1429-1433 (2009). PDF preprint
S. Liang, D.J. Jeffrey: Comparison of homotopy analysis method and homotopy perturbation method through an evolution equation. Communicatons Nonlinear Science Numerical Simulation, Vol 14, pp 4057-4064, 2009. PDF preprint
A.D. Rich, D.J. Jeffrey: A knowledge repository for indefinite integration based on transformation rules. In: Intelligent Computer Mathematics, LNCS 5625, pp480-485, Springer 2009. PDF preprint
S. Liang, D.J. Jeffrey: Automatic computation of the complete root classification for a parametric polynomial. J. Symbolic Computation, Vol 44, pp 1487-1501 (2009). PDF preprint
S. Liang, D.J. Jeffrey, M. Moreno Maza: The complete root classification of a parametric polynomial on an interval. In: Proceedings of ISSAC 2008, pp 189-196, ACM Press 2008. PDF offprint
S. Liang, D.J. Jeffrey: Unconstrained parametric minimization of a polynomial: approximate and exact. Proc. ASCM 2007. LNAI 5081, Springer, pp22--31. PDF preprint.
W. Zhou, D.J. Jeffrey: Fraction-free matrix factors: new forms for LU and QR factors. Frontiers in Computer Science in China, Vol 2, no. 1, pp67--80, 2008. PDF preprint
S. Liang, D.J. Jeffrey: Automatic computation of the travelling wave solutions to nonlinear PDEs. Computer Physics Communications, Vol 178, issue 9, pp700-712, 2008. PDF offprint.
D.J. Jeffrey: Watch out for discontinuous integrals. In: Computer Algebra in Education, edited by Michael J. Wester and Michel Beaudin, Aulonna Press, White Lake. ISBN 978-0-9754541-9-6. pp71-80, 2008.
R.M. Corless, H. Ding, N.J. Higham, D.J. Jeffrey: The solution of S*exp(S)=A is not always the Lambert W function of A. In: "ISSAC 2007", Editor C.W.Brown, pp 116--121, ACM Press, 2007. PDF preprint.
S. Liang and D.J. Jeffrey: Rule-based simplification in vector-product spaces. (Calculemus 2007). In: LNAI 4573, pp. 116-127, 2007. PDF preprint.
D.J. Jeffrey, S. Ilie, J.M. Gardiner, S.W. Campbell: A Symbolic--Numeric Approach to an Electric Field Problem. In "Symbolic-Numeric Computation", Eds Dongming Wang, Lihong Zhi. Trends in Mathematics, Birkhauser, pp 349--359, 2007. PDF preprint
W. Zhou, D.J. Jeffrey, G. Reid: Symbolic Computation Sequences and Numerical Analytic Geometry Applied to Multibody Dynamical Systems. In "Symbolic-Numeric Computation", Eds Dongming Wang, Lihong Zhi. Trends in Mathematics, Birkhauser, pp 335-347, 2007. PDF preprint
S. Liang, D.J. Jeffrey: An algorithm for computing the complete root classification of a parametric polynomial. Proceedings AISC 2006. LNCS 4120, Eds. J. Calmet, T.Ida, D. Wang. pp116-130, Springer 2006.
W. Zhou, J. Carette, D.J. Jeffrey, M.B. Monagan: Hierarchical representations with signatures for large expression management. Proceedings AISC 2006. LNCS 4120, Eds. J. Calmet, T.Ida, D. Wang. pp254-268, Springer 2006.
M. Bronstein, R.M. Corless, J.H. Davenport, D.J. Jeffrey: Algebraic properties of the Lambert W Function from a result of Rosenlicht and of Liouville. Integral Transforms and Special Functions, Vol 19(10), pp 709-712, 2008. PDF preprint
J. Carette, W. Zhou, D.J. Jeffrey, M.B. Monagan: Linear Algebra using Maple's LargeExpressions package. Proceedings of Maple Conference, pp. 14-25, 2006.
W. Zhou, D.J. Jeffrey, R.M. Corless: Fraction-free forms of LU matrix factoring. In: Computer Algebra in Education. Edited by Michael J. Wester and Michel Beaudin. Aulonna Press, White Lake. pp37-42, 2008.
S. Liang, D.J. Jeffrey, S.M. Watt: Component-free vector algebra in Aldor. Proceedings Transgressive Computing 2006.
D.J. Jeffrey and R.M. Corless: Linear Algebra in Maple. In "CRC Handbook of Linear Algebra", Ed L. Hogben. Chapter 72, pp 1-21, 2006. PDF proof copy
V. Elias, S. Homayouni and D.J. Jeffrey: Diminished upper bounds on the unification mass-scale for heavy Higgs boson masses, Modern Physics Letters A 21, pp 209--212, 2006. PDF proof
Frederic Alfonsi and D.J. Jeffrey: A model for plate clash in disk refiners. Preprints for 92nd Technical Meeting Pulp and Paper Association. (PAPTAC 2006) PDF preprint
D.J. Jeffrey, Pratibha and K.B. Roach: Affine transformations of algebraic numbers. Proceedings ISSAC 2005, Beijing, China. ACM Press. pp.193--199. PDF preprint
D.J. Jeffrey and S. Ilie: An inclusion in a microchannel of a porous medium. In Environmental Fluid Mechanics, Editor: S.N. Bora, Allied Publishers, 2005 (ISBN 81-7764-788-1). pp.112-116.
W. Zhou, D.J. Jeffrey and G.J. Reid: An Algebraic Method for Analyzing Open-Loop Dynamic Systems. Proceedings ICCS2005, Editors V.S. Sunderam, G.D. van Albada, P.M.A. Sloot, J.J. Dongarra. Springer LNCS 3516, 2005, pp 586--593. PDF preprint
W. Zhou, D.J. Jeffrey, G.J. Reid, C. Schmitke and J. McPhee: Implicit Reduced Involutive Forms and Their Application to Engineering Multibody Systems. Proceedings IWMM 2004, Edited by Hongbo Li, Peter J. Olver, Gerald Sommer. Springer LNCS 3519, 2005, pp 31-- 43. ISBN: 3-540-26296-2. PDF preprint
Pratibha and D.J. Jeffrey: Stokes-Flow Problem Solved using Maple. Proceedings ICCS2005, Editors V.S. Sunderam, G.D. van Albada, P.M.A. Sloot, J.J. Dongarra. Springer LNCS 3516, 2005, pp 667--670. PDF preprint
S. Ilie and D.J.Jeffrey: A note on Laplace's equation inside a cylinder. Applied Mathematics Letters, Vol 18 (1), pp 55--59, 2005. PDF preprint
D.J. Jeffrey and A.C. Norman: Not seeing the roots for the branches. SIGSAM Bulletin, Vol 38(3), issue 149, pp 57--66, 2004. PDF offprint
V.S. Adamchik and D.J. Jeffrey: Polynomial transformations of Tschirnhaus, Bring and Jerrard. SIGSAM Bulletin, Vol 37 (3), issue 145, pp 90--93, 2003. PDF reprint
D.J. Jeffrey: The art of formula. Algorithmic Algebra and Logic 2005, Eds Dolzmann, Seidl, Sturm. ISBN 3-8334-2669-1, Norderstedt, Germany. pp. 135--140. PDF pre-print.
K. Hazaveh, D.J. Jeffrey, G.J. Reid, S.M. Watt, A.D. Wittkopf: An exploration of homotopy solving in Maple. Proc. ASCM 2003, Beijing. pp 145--162. PDF pre-print.
D.J. Jeffrey: High precision computation of elementary functions in Maple. Proceedings of Computer Algebra in Scientific Computation 2002. pp 183--190. Published by Technische Universitat, Munchen. PDF pre-print.
R.M. Corless, D.J. Jeffrey: The Wright omega function. Artificial Intelligence, Automated Reasoning, and Symbolic Computation. (Editors: J. Calmet, B. Benhamou, O. Caprotti, L. Henocque, V. Sorge). AISC-Calculemus 2002. LNAI 2385, Springer. pp 76--89, 2002. PDF preprint.
D.J. Jeffrey: The multivalued nature of inverse functions. Postscript preprint.
D.J. Jeffrey, R.M. Corless: Teaching linear algebra with and to computers. Proceedings of ATCM 2001. ISBN 0-86459-182-9, 2001, pp 120--129. Postscript preprint.
R.J.Bradford, R.M.Corless, J.H.Davenport, D.J.Jeffrey, S.M. Watt: Reasoning about the elementary functions of complex analysis. Annals Maths Artificial Intelligence, vol 36, 2002, pp 303-318. PDF preprint.
D.J. Jeffrey, M.W. Giesbrecht, R.M. Corless: Integer roots for integer-power-content calculations. In: Computer mathematics, proceedings of the fourth Asian symposium. Editors: Xiao-shan Gao and Dongming Wang. World Scientific, Lecture Notes Series on Computing, Vol 8, 2000, pp 71 -- 74. PDF preprint.
R.M. Corless, J.H. Davenport, D.J. Jeffrey, G. Litt, S.M. Watt: Reasoning about the elementary functions of complex analysis. In: Artificial Intelligence and Symbolic Computation (ed. J.A. Campbell and E. Roanes-Lozano), Springer lecture notes on Artificial Intelligence (LNAI) vol 1930, pp 115-126. Springer-Verlag 2001. ISBN 3-540-42071-1. PDF preprint.
R.M. Corless, J.H. Davenport, D.J. Jeffrey, S.M. Watt: According to Abramowitz and Stegun, SIGSAM Bulletin, Vol 34 (2), pp 58--65. PDF version.
S.R. Valluri, D.J. Jeffrey, R.M. Corless: Some applications of the Lambert W function to physics. Canadian J. Physics, vol 78, pp823-831 (2000). PDF version.
D.J. Jeffrey, A.D. Rich: Simplifying square roots of square roots by denesting. In: "Computer algebra systems: a practical guide", edited by M.J. Wester, pp 61-72, Wiley 1999. PDF preprint.
R.M. Corless, M. Geisbrecht, D.J. Jeffrey, S.M. Watt: Approximate polynomial decomposition. In: ISSAC99, Proceedings of the 1999 International Symposium on Symbolic and Algebraic Computation, Edited by Sam Dooley. pp 213-219. ACM Press 1999. PDF format.
D.J. Jeffrey, D.E.G. Hare, R.M. Corless: Exact rational solutions of a transcendental equation. C.R. Math. Rep. Acad. Sci. Canada Vol 20 (3), pp71-76 (1998). PDF version.
R.M. Corless, D.J. Jeffrey: Graphing elementary Riemann surfaces. SIGSAM Bulletin, Vol 32(1), issue 123, pp11-17 (1998). PDF version.
R.M. Corless, D.J. Jeffrey, M.B. Monagan, Pratibha: Two perturbation calculations in fluid mechanics using large expression management. J. Symbolic Computation, Vol 23 (4), pp427-443 (1997). PDF version.
R.M. Corless, D.J. Jeffrey: The Turing factorization of a rectangular matrix. SIGSAM Bulletin, vol 31(3), pp20-28 (1997). PDF version.
D.J. Jeffrey, A.D. Rich: Recursive integration of piecewise-continuous functions. In: ISSAC98, Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation, Edited by O. Gloor. pp 290-294. ACM Press 1998. PDF version.
D.J. Jeffrey, G. Labahn, M.v. Mohrenschildt, A.D. Rich: Integration of the signum, piecewise and related functions. In: ISSAC97, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, Edited by W.W.Kuechlin. pp 324-330. ACM Press 1997. PDF version.
R.M. Corless, D.J. Jeffrey, D.E. Knuth: A sequence of series for the Lambert W function. In: ISSAC97, Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation, Edited by W.W.Kuechlin. ACM Press 1997. PDF preprint
R.M. Corless, D.J. Jeffrey: Scientific computing: one part of the revolution. J. Symbolic Computation, vol 11, pp485-495, (1997).
D.J. Jeffrey: Formulae, algorithms, and quartic extrema. Mathematics Magazine 70, pp349 - 356 (1997). Postscript version
D.J. Jeffrey: Rectifying transformations for the integration of rational trigonometric functions. J. Symbolic Computation 24, 563 - 573 (1997). PDF version.
D.J. Jeffrey: Some basic principles in interaction calculations. In: "Sedimentation of small particles in a viscous fluid", edited by E.M.Tory, pp 97 - 124. Computational Mechanics Publications, Southampton (ISBN 1562522809) 1996. PDF version.
D.J. Jeffrey, D.E.G.Hare, Robert M. Corless: Unwinding the branches of the Lambert W function. Math. Scientist. 21, 1 - 7 (1996). PDF version
R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth: On the Lambert W function. Adv. Computational Maths. 5, 329 - 359 (1996). PDF version.
R.M. Corless, D.J. Jeffrey, Editors' corner: The unwinding number. SIGSAM Bulletin 116 (1996). PDF version
A.D. Rich, D.J. Jeffrey, Function evaluation on branch cuts. SIGSAM Bulletin 116, p25-27 (1996). PDF version.
D.J.Jeffrey, R.M. Corless, D.E.G. Hare, D.E. Knuth, Sur l'inversion de y^a e^y au moyen des nombres de Stirling associes. Comptes Rendus Acad. Sci. Paris, t. 320, Serie I, p1449-1452 (1995). French as PDF ; English as PDF.
D.J.Jeffrey, A.D.Rich, The evaluation of trigonometric integrals avoiding spurious discontinuities. ACM Transactions on Mathematical Software, 20, pp 124 - 135 (1994). PDF version
D.J.Jeffrey, The importance of being continuous, Mathematics Magazine, Vol 67, pp 294 - 300 (1994). PDF version
S. Kocabiyik, D.J. Jeffrey, Asymptotic analysis of interactions between highly conducting cylinders, Applied Mathematics Letters, Vol 7, no 6, pp 59 - 63 (1994). PDF version.
D.J.Jeffrey: Integration to obtain expressions valid on domains of maximum extent, Proceedings of ISSAC 93, Edited by M. Bronstein, ACM Press, 1993, pp 34 - 41. PDF version.
R.M. Corless, D.J. Jeffrey and H. Rasmussen: Numerical evaluation of Airy functions with complex arguments, J. Computational Phys., Vol 99, no. 1, pp 106 - 114, 1992. PDF version.
R.M.Corless, D.J.Jeffrey: Well... it isn't quite that simple, SIGSAM Bulletin, vol 26(3), pp2-6, 1992. PDF version.
R.M.Corless and D.J.Jeffrey: Solution of a hydrodynamic lubrication problem with Maple, J. Symb. Comp. Vol 9, pp 503--513, 1990. Scanned PDF of paper.
D.J.Jeffrey: Higher-order corrections to the axisymmetric interactions of nearly touching spheres. Phys Fluids A, Vol 1, pp 1740--1742, 1989. Scanned PDF of paper.
R.M.Corless and D.J.Jeffrey: Stress moments of nearly touching spheres in low Reynolds number flow, J. Appl. Maths Phys. (ZAMP), Vol 39, pp 874--884, 1988. Scanned PDF of paper.
D.J.Jeffrey and R.M.Corless: Forces and stresslets for the axisymmetric motion of nearly touching unequal spheres, PCH PhysicoChemical Hydrodynamics Vol 10(4), 461--470, 1988. Scanned PDF of paper.
D.J.Jeffrey and Y.Onishi: The forces and couples acting on two nearly touching spheres in low-Reynolds-number flow, J.Appl. Maths Phys (ZAMP), Vol 35, pp 634--641, 1984. Scanned PDF of paper.
D.J.Jeffrey and Y. Onishi: The slow motion of a cylinder next to a plane wall. QJMAM, Vol34(2), pp.129--137, 1981. Scanned PDF.
D.J.Jeffrey: The temperature field or electric potential around two almost-touching spheres. J. Inst. Maths Applics. Vol 22, pp. 337--351, 1978. Scanned PDF.
D.J. Jeffrey: The physical significance of non-convergent integrals in expressions for effective transport properties, In: Continuum Models of Discrete Systems, edited by J.W. Provan, University of Waterloo Press, pp 653--673, 1977. Re-typed PDF version.