David Borwein's papers

We give below a list of 160 papers by David Borwein. We note that J M Borwein is his son Jonathan Michael Borwein, P Borwein is his younger son Peter Benjamin Borwein, and B Borwein is his wife Bessie Borwein. B L R Shawyer is his St Andrews Ph.D. student Bruce Lockhart Robertson Shawyer (Ph.D. 1963) who later became his colleague at the University of Western Ontario. The following, who are joint authors, were Ph.D. students of David Borwein at the University of Western Ontario: Frank Cass (Ph.D. 1967); Robert Phillips (Ph.D. 1968); Syed Rizv (Ph.D. 1969); Irvine Robinson (Ph.D. 1969); Eddy Smet (Ph.D. 1973); Bruce Watson (Ph.D. 1974); Kenneth Roberts (Ph.D. 1979); John Sayre (Ph.D. 1982); Tom Markovich (Ph.D. 1986); and Xiaopeng Gao (Ph.D. 1994).

D Borwein, On the Cesàro summability of integrals, J. London Math. Soc. 25 (1950), 289-302.
D Borwein, A summability factor theorem, J. London Math. Soc. 25 (1950), 302-315.
D Borwein, On the absolute Cesàro summability of integrals, Proc. London Math. Soc. (3) 1 (1951), 308-326.
David Borwein, Note on summability factors, J. London Math. Soc. 29 (1954), 198-206.
D Borwein, Integration by parts of Cesàro summable integrals, J. London Math. Soc. 29 (1954), 276-292.
D Borwein, On the absolute summability of Stieltjes integrals, J. London Math. Soc. 29 (1954), 476-486.
D Borwein, On the abscissae of summability of a Dirichlet series, J. London Math. Soc. 30 (1955), 68-71.
D Borwein, A theorem on Riesz summability, J. London Math. Soc. 31 (1956), 319-324.
D Borwein, On a scale of Abel-type summability methods, Proc. Camb. Phil. Soc. 53 (1957), 318-322.
D Borwein, On methods of summability based on power series, Proc. Royal Soc. Edinburgh 64 (1957), 342-349.
D Borwein, A logarithmic method of summability, J. London Math. Soc. 33 (1958), 212-220.
D Borwein, On products of sequences, J. London Math. Soc. 33 (1958), 352-357.
D Borwein, Theorems on some methods of summability, Quart. J. Math. Oxford (2) 9 (1958), 310-316.
D Borwein, On multiplication of (C, μ)-summable series, J. London Math. Soc. 33 (1958), 441-449.
D Borwein, On Borel-type methods of summability, Mathematika 5 (1958), 128-133.
D Borwein, On methods of summability based on integral functions, Proc. Camb. Phil. Soc. 55 (1959), 23-30.
D Borwein and A V Boyd, Binary and ternary transformations of sequences, Proc. Edinburgh Math. Soc. 11 (1959), 175-181.
D Borwein and A R Mitchell, On finite difference solutions of two point boundary value problems, ZAMP 10 (1959), 221-232.
D Borwein, An extension of a theorem on the equivalence between absolute Rieszian and absolute Cesàro summability, Proc. Glasgow Math. Assoc. 4 (1959), 81-83.
D Borwein, Relations between Borel-type methods of summability, J. London Math. Soc. 35 (1960), 65-70.
On moment constant methods of summability, J. London Math. Soc. 35 (1960), 71-77.
D Borwein, On methods of summability based on integral functions II, Proc. Camb. Phil. Soc. 56 (1960), 125-131.
D Borwein, On strong and absolute summability, Proc. Glasgow Math. Assoc. 4 (1960), 122-139.
D Borwein, Nörlund methods of summability associated with polynomials, Proc. Edinburgh Math. Soc. (2) 12 (1960), 7-15.
D Borwein and B L R Shawyer, On Riesz summability factors, Proc. Glasgow Math. Assoc. 5 (1962), 188-196.
D Borwein and Y Matsuoka, On multiplication of Cesàro summable series, J. London Math. Soc. 38 (1963), 393-400.
D Borwein and B L R Shawyer, On absolute Riesz summability factors, J. London Math. Soc. 39 (1964), 455-465.
D Borwein and B L R Shawyer, On strong Riesz summability factors, J. London Math. Soc. 40 (1965), 111-126.
D Borwein, Linear functionals connected with strong Cesàro summability, J. London Math. Soc. 40 (1965), 628-634.
D Borwein, On a class of convergent series of positive terms, J. London Math. Soc. 40 (1965), 587-588.
D Borwein, On a non-enumerable exceptional set, Amer. Math. Monthly 73 (1966), 288.
D Borwein, On a generalised Cesàro summability method of integral order, Tohoku Math. J. (2) 18 (1966), 71-73.
D Borwein and B L R Shawyer, On Borel-type methods, Tohoku Math. J. 18 (1966), 283-298.
M Aoyagi, D Borwein and A Meir, Problems and Solutions: Solutions of Advanced Problems: 5333, Amer. Math. Monthly 73 (9) (1966), 1022-1024.
D Borwein, On a method of summability equivalent to the Cesàro method, J. London Math. Soc. 42 (1967), 339-343.
D Borwein and D C Russell, On Riesz and generalised Cesàro summability of arbitrary positive order, Math. Z. 99 (1967), 171-177.
D Borwein and B L R Shawyer, On Borel-type methods II, Tohoku Math. J. (2) 19 (1967), 232-237.
D Borwein and B L R Shawyer, Correction "On Borel-type methods", Tohoku Math. J. (2) 19 (1967), 244.
D Borwein, On generalised Cesàro summability, J. Indian Math. Soc. (Prasad Memorial Issue) 9 (1967), 55-64.
D Borwein and F P A Cass, Strong Nörlund summability, Math. Z. 103 (1968), 94-111.
D Borwein and F P A Cass, Multiplication theorems for strong Nörlund summability, Math. Z. 107 (1968), 33-42.
D Borwein and R Phillips, Scales of logarithmic methods of summability, Canad. Math. Bull. 12 (1969), 445-452.
D Borwein, A tauberian theorem for Borel-type methods of summability, Canad. J. Math. 21 (1969), 740-747.
D Borwein and A Meir, A property of gradients, Amer. Math. Monthly 76 (1969), 648.
D Borwein, On Riesz and generalised Cesàro summability, J. London Math. Soc. (2) 2 (1970), 61-66.
D Borwein, On absolute Borel-type methods of summability, Proc. Amer. Math. Soc. 24 (1970), 85-89.
D Borwein and J H Rizvi, On Abel-type methods of summability, J. Reine Angew. Math. 247 (1971), 139-145.
D Borwein, Convergence criteria for bounded sequences, Proc. Edinburgh Math. Soc. (2) 19 (1972), 99-103.
D Borwein and A Meir, Divergence criteria for positive series, Amer. Math. Monthly 79 (1972), 1104-1106.
D Borwein and J H Rizvi, On strong summability, J. Reine Angew. Math. 260 (1973), 119-126.
D Borwein and H Kestelman, Problems and Solutions: Solutions of Advanced Problems: 5846, Amer. Math. Monthly 80 (6) (1973), 698-699.
D Borwein and F P A Cass, Strict inclusion between strong and ordinary methods of summability, J. Reine Angew. Math. 267 (1974), 166-174.
D Borwein and E F M Smet, Tauberian theorems for Borel-type methods of summability, Canad. Math. Bull. 17 (1974), 167-173.
D Borwein and I J W Robinson, A tauberian theorem for Borel-type methods of summability, J. Reine Angew. Math. 273 (1975), 153-164.
D Borwein and J H Rizvi, Generalized strong summability of infinite series, J. Reine Angew. Math. 276 (1975), 142-147.
D Borwein, Problems and Solutions: Solutions of Advanced Problems: 5880, Amer. Math. Monthly 82 (8) (1975), 857-858.
D Borwein and F P A Cass, Equivalence of Riesz methods of summability, J. London Math. Soc. (2) 13 (1976), 205-208.
D Borwein and B B Watson, A tauberian theorem for Abelian summability methods, J. Reine Angew. Math. 285 (1976), 75-76.
D Borwein and B L R Shawyer, On functional Cesàro and Hölder methods of summability, Canad. J. Math. 28 (5) (1976), 1058-1061.
D Borwein and E F M Smet, Addendum to "Tauberian theorems for Borel-type methods of summability", Canad. Math. Bull. 19 (2) (1976), 245-246.
D Borwein and W Kratz, On the zeros of the power series $\sum _{n=0}^{∞} (-1)^{n}(1-c^{-n-1})^{\kappa}z^{n}$ with an application to discontinuous Riesz-summability, Canad. Math. Bull. 19 (4) (1976), 417-424.
D Borwein and E F M Smet, Tauberian theorems for strong and absolute Borel-type methods of summability, Canad. Math. Bull. 20 (2) (1977), 161-172.
D Borwein and W Gawronski, On certain sequences of plus and minus ones, Canad. J. Math. 30 (1) (1978), 170-179.
D Borwein, A sum of reciprocals of least common multiples, Canad. Math. Bull. 21 (1) (1978), 117-118.
D Borwein and B B Watson, Tauberian theorems on a scale of Abel-type summability methods, J. Reine Angew. Math. 298 (1978), 1-7.
D Borwein and S Z Ditor, Translates of sequences in sets of positive measure, Canad. Math. Bull. 21 (4) (1978), 497-498.
D Borwein, The Hausdorff moment problem, Canad. Math. Bull. 21 (3) (1978), 257-265.
D Borwein and H D Ruderman, Problems and Solutions: Solutions of Advanced Problems: 6105, Amer. Math. Monthly 85 (3) (1978), 207-208.
D Borwein, Corrections "The Hausdorff moment problem", Canad. Math. Bull. 22 (1979), 128.
D Borwein and A Jakimovski, Matrix operators on $l^{p}$ , Rocky Mountain J. Math. 9 (3) (1979), 463-477.
D Borwein and D M Milosevic, Problems and Solutions: Solutions of Advanced Problems: 6227, Amer. Math. Monthly 87 (4) (1980), 311-312.
B Borwein, D Borwein, J Medeiros, and J McGowan, The ultrastructure of monkey foveal photoreceptors, with special reference to the structure, shape, size, and spacing of the foveal cones, Amer. J. Anatomy 159 (2) (1980), 125-146.
D Borwein and B Watson, On the relation between the logarithmic and Borel-type summability methods, Canad. Math. Bull. 24 (2) (1981), 153-159.
D Borwein and P F A Cass, Weighted means, generalised Hausdorff matrices and the Borel property, Acta Math. Hung. 37 (1-3) (1981), 29-34.
D Borwein, Tauberian conditions for the equivalence of weighted mean and power series methods of summability, Canad. Math. Bull. 24 (3) (1981), 309-316.
D Borwein, Matrix transformations of weakly multiplicative sequences of random variables, J. London Math. Soc. (2) 23 (2) (1981), 363-371.
D Borwein and A Jakimovski, Generalization of the Hausdorff moment problem, Canad. J. Math. 33 (4) (1981), 946-960.
D Borwein and A Jakimovski, Corrections "Matrix operators on $l^{p}$ ", Rocky Mountain J. Math. 11 (1) (1981), 154.
D Borwein and A Jakimovski, Generalization of the Hausdorff moment problem, in S P Singh and J H Burry, Nonlinear Analysis and Applications, Proceedings of International Conference on Nonlinear Analysis and Applications, St John's, Newfoundland, 1981 (Routledge, 1982), 33-37.
D Borwein and B Watson, Tauberian theorems between the logarithmic and Abel-type summability methods, Pacific J. Math. 101 (1) (1982), 11-23.
D Borwein and K Roberts, On summability factors for the strong Cesàro method for integrals, Analysis 2 (1-4) (1982), 7-42.
D Borwein and A Jakimovski, Transformations of certain sequences of random variables by generalized Hausdorff matrices, Pacific J. Math. 107 (1) (1983), 15-26.
D Borwein, Generalized Hausdorff matrices as bounded operators on $l^{p}$ , Math. Z. 183 (4) (1983), 483-487.
D Borwein and F Peter Cass, Nörlund matrices as bounded operators on $l_{p}$ , Arch. Math. 42 (5) (1984), 464-469.
R L Cooke, D Borwein and P Borwein, Problems and Solutions: Solutions of Advanced Problems: 6299, Amer. Math. Monthly 91 (4) (1984), 259-260.
D Borwein and B Thorpe, Conditions for inclusion between Nörlund summability methods, Acta Math. Hung. 45 (1-2) (1985), 151-158.
D Borwein, Jonathan M Borwein and Keith F Taylor, Convergence of lattice sums and Madelung's constant, J. Math. Phys. 26 (11) (1985), 2999-3009.
D Borwein and B Thorpe, On Cesàro and Abel summability factors for integrals, Canad. J. Math. 38 (2) (1986), 453-477.
D Borwein, F Peter Cass and John E Sayre, On absolute generalized Hausdorff summability, Arch. Math. 46 (5) (1986), 419-427.
D Borwein and J Borwein, A note on alternating series in several dimensions, Amer. Math. Monthly 93 (7) (1986), 531-539.
D Borwein, F Peter Cass and John E Sayre, On generalized Hausdorff matrices, J. Approx. Theory 48 (4) (1986), 354-360.
D Borwein and A Meir, A Tauberian theorem concerning weighted means and power series, Math. Proc. Camb. Phil. Soc. 101 (2) (1987), 283-286.
D Borwein, Tauberian and other theorems concerning Dirichlet's series with non-negative coefficients, Math. Proc. Camb. Phil. Soc. 102 (3) (1987), 517-532.
D Borwein and T Markovich, A Tauberian theorem concerning Borel-type and Cesàro methods of summability, Canad. J. Math. 40 (1) (1988), 228-247.
D Borwein and T Markovich, On Cesàro and Borel-type summability, Proc. Amer. Math. Soc. 103 (4) (1988), 1108-1112.
D Borwein, J M Borwein, R Shail and I J Zucker, Energy of static electron lattices, J. Math. Phys. 21 (7) (1988), 1519-1531.
D Borwein, S A Rankin and L E Renner, Enumeration of injective partial transformations, Discrete Math. 73 (3) (1989), 291-296.
D Borwein, F Peter Cass and John E Sayre, On strong generalized Hausdorff summability, Acta Math. Hung. 53 (1-2) (1989), 95-101.
D Borwein and Werner Kratz, On relations between weighted mean and power series methods of summability, J. Math. Analysis and Applications 139 (1) (1989), 178-186.
D Borwein, A Tauberian theorem concerning Dirichlet series, Math. Proc. Camb. Phil. Soc. 105 (3) (1989), 481-484.
D Borwein, J M Borwein and R Shail, Analysis of certain lattice sums, J. Math. Analysis and Applications 143 (1) (1989), 126-137.
D Borwein, Tauberian theorems concerning Laplace transforms and Dirichlet series, Arch. Math. 53 (4) (1989), 352-362.
D Borwein, An inclusion theorem for Dirichlet series, Canad. Math. Bull. 32 (4) (1990), 479-481.
D Borwein, Asymptotic relationships between Dirichlet series, J. Math. Analysis and Applications 147 (2) (1990), 604-609.
D Borwein and J M Borwein, Fixed point iterations for real functions, J. Math. Analysis and Applications 157 (1) (1991), 112-126.
D Borwein, The non-local nature of the summability of Fourier series by certain absolute Riesz methods, Israel Mathematical Conference Proceedings 4 (Bar-Ilan University, Gelbart Research Institute for Mathematical Sciences, Ramat Gan, 1991), 69-72.
D Borwein and E Ehrhart, Problems and Solutions: Solutions of Advanced Problems: 6605, Amer. Math. Monthly 98 (3) (1991), 276-277.
D Borwein and T Markovich, A Weighted means and summabiltiy by the circle and other methods, J. Approximation Theory 68 (1) (1992), 49-55.
D Borwein, The non-local nature of the summability of Fourier series by certain absolute Riesz methods, Proc. Amer. Math. Soc. 114 (1) (1992), 89-94.
D Borwein, A Tauberian theorem concerning Borel-type and Riesz summability methods, Canad. Math. Bull. 35 (1) (1992), 14-20.
D Borwein, Tauberian theorems concerning power series with non-negative coefficients, Acta Mathematica Hungarica 59 (1-2) (1992), 85-89.
M Cook, D Borwein, W Janous and E Marcin, Problems and Solutions: Solutions: E3388, Amer. Math. Monthly 99 (1) (1992), 69-70.
D Borwein, Nörlund operators on $l_{p}$ , Canad. Math. Bull. 36 (1) (1993), 8-14.
D Borwein and X Gao, Generalized Hausdorff and weighted mean matrices as operators on $l_{p}$ , J. Math. Analysis and Applications 178 (2) (1993), 517-528.
H Alzer, D Borwein, J Borwin, et.al., Problems and Solutions: Problems: 10330-10337, Amer. Math. Monthly 100 (8) (1993), 796-798.
D Borwein and W Kratz, An O-Tauberian theorem and a high indices theorem for power series methods of summability, Math. Proc. Camb. Phil. Soc. 115 (2) (1994), 365-375.
D Borwein and R Kiesel, Weighted means and summability by generalized Nörlund and other methods, J. Math. Analysis and Applications 184 (3) (1994), 607-619.
D Borwein and X Gao, Matrix operators on $l_{p}$ to $l_{q}$ , Canad. Math. Bull. 37 (4) (1994), 448-456.
D Borwein and A Jakimovski, Matrix transformations of power series, Proc. Amer. Math. Soc. 122 (2) (1994), 511-523.
D Borwein and J M Borwein, On some trigonometric and exponential lattice sums, J. Math. Analysis and Applications 188 (1) (1994), 209-218.
D Borwein and J M Borwein, On an intriguing integral and some series related to $\zeta(4)$ , Proc. Amer. Math. Soc. 123 (4) (1995), 1191-1198.
D Borwein, J M Borwein and R Girgensohn, Explicit evaluation of Euler sums, Proc. Edinburgh Math. Soc. (2) 38 (2) (1995), 277-294.
D Borwein, P Borwein and A Jakimovksi, Matrix transformations of series of orthogonal polynomials, Mathematika 42 (2) (1995), 427-443.
D Borwein, J M Borwein, P Borwein and R Girgensohn, Giuga's conjecture on primality, Amer. Math. Monthly 103 (1) (1996), 40-50.
D Borwein, J M Borwein and X Wang, Approximate subgradients and coderivatives in $\mathbb{R}^{n}$ , Set-Valued Analysis 4 (4) (1996), 375-398.
D Borwein, J Borwein, H-J Seiffert, R D Brown and P Szeptycki, Problems and Solutions: Solutions: 10335, Amer. Math. Monthly 104 (1) (1997), 72-74.
D Borwein and K-W Chen, Problems and Solutions: Solutions: 10416, Amer. Math. Monthly 104 (5) (1997), 464-465
D Borwein, J M Borwein and C Pinner, Convergence of Madelung-like lattice sums, Trans. Amer. Math. Soc. 350 (8) (1998), 3131-3167.
D Borwein, Simple conditions for matrices to be bounded operators on $l_{p}$ , Canad. Math. Bull. 41 (1) (1998), 10-14.
D Borwein and A Jakimovski, A generalization of Hardy's inequality with applications, Communications in Applied Analysis 2 (3) (1998), 309-320.
D Borwein and W Kratz, A high indices Tauberian theorem, Acta. Sci. Math. (Szeged) 64 (1-2) (1998), 143-149.
D Borwein and A Jakimovski, Matrices that commute with certain Hausdorff matrices, Analysis 18 (3) (1998), 227-244.
J Beurer, D Borwein and W Kratz, Two Tauberian theorems for Dirichlet series methods of summability, Acta. Sci. Math. (Szeged) 65 (1-2) (1999), 139-168.
D Borwein, Weighted mean operators on $l_{p}$ , Canad. Math. Bull. 43 (4) (2000), 406-412.
D Borwein, J M Borwein and P Maréchal, Surprize maximization, Amer. Math. Monthly 107 (6) (2000), 517-527.
D Borwein and J M Borwein, Some remarkable properties of sinc and related integrals, Ramanujan J. 5 (1) (2001), 73-89.
D Borwein, W Kratz and U Stadtmüller, One-sided Tauberian theorems for Dirichlet series methods of summability, Rocky Mountain J. Math. 31 (3) (2001), 797-830.
D Borwein, J M Borwein, G Fee and R Girgensohn, Refined convexity and special cases of the Blaschke-Santalo inequality, Math. Inequalities and Applications 4 (4) (2001), 631-638.
D Borwein, J M Borwein and B A Mares Jr., Multi-variable sinc integrals and volumes of polyhedra, Ramanujan J. 6 (2) (2002), 189-208.
D Borwein and W Kratz, A one-sided Tauberian theorem for the Borel summability method, J. Math. Analysis and Applications 293 (1) (2004), 285-292.
D Borwein, J M Borwein and W F Galway, Finding and excluding $b$ -ary Machin-type individual digit formulae, Canad. J. Math. 56 (5) (2004), 897-925.
D Borwein and W Kratz, Weighted convolution operators on $l_{p}$ , Canad. Math. Bull. 48 (2) (2005), 175-179.
D Borwein, J M Borwein and D M Bradley, Parametric Euler sum identities, J. Math. Anal. Appl. 316 (1) (2006), 328-338.
D Borwein, J M Borwein, R Crandall and R Mayer, On the dynamics of certain recurrence relations, Ramanujan J. 13 (1-3) (2007), 63-101.
D Borwein and J M Borwein, van der Pol expansions of $L$ -series, Canad. Math. Bull. 50 (1) (2007), 11-23.
D H Bailey, D Borwein, J M Borwein and R Crandall, Hypergeometric forms for Ising-class integrals, Experiment. Math. 16 (3) (2007), 257-276.
D Borwein, J M Borwein and O-Y Chan, The evaluation of Bessel functions via exp-arc integrals, The evaluation of Bessel functions via exp-arc integrals, J. Math. Anal. Appl. 341 (1) (2008), 478-500.
D Borwein, J M Borwein and R E Crandall, Effective Laguerre asymptotics, SIAM J. Numer. Anal. 46 (6) (2008), 3285-3312.
R Baillie, D Borwein and J M Borwein, Surprising sinc sums and integrals, Amer. Math. Monthly 115 (10) (2008), 888-901.
D Borwein, J M Borwein and I E Leonard, $L_{p}$ norms and the sinc function, Amer. Math. Monthly 117 (6) (2010), 528-539.
D Borwein, J M Borwein, M L Glasser and J G Wan, Moments of Ramanujan's generalized elliptic integrals and extensions of Catalan's constant, J. Math. Anal. Appl. 384 (2) (2011), 478-496.
D Borwein, J M Borwein and A Straub, A sinc that sank, Amer. Math. Monthly 119 (7) (2012), 535-549.
T Amdeberhan, D Borwein, J M Borwein and A Straub, On formulas for π experimentally conjectured by Jauregui-Tsallis, J. Math. Phys. 53 (7) (2012).
D Borwein, J M Borwein, A Straub and J Wan, Log-sine evaluations of Mahler measures, II, Integers 12 (6) (2012), 1179-1212.
D Borwein, Criteria for the sequence of differences of a bounded sequence to be null, Bull. Aust. Math. Soc. 88 (1) (2013), 123-127.
D Borwein, J M Borwein and A Straub, On lattice sums and Wigner limits, J. Math. Anal. Appl. 414 (2) (2014), 489-513.
D Borwein, J M Borwein and B Sims, On the solution of linear mean recurrences, Amer. Math. Monthly 121 (6) (2014), 486-498.
D Borwein and J M Borwein, Deriving new sinc results from old, Amer. Math. Monthly 121 (8) (2014), 700-705.
D H Bailey, D Borwein and J M Borwein, On Eulerian log-gamma integrals and Tornheim-Witten zeta functions, Ramanujan J. 36 (1-2) (2015), 43-68.
D Borwein, J M Borwein and B Sims, Symmetry and the monotonicity of certain Riemann sums, Springer Proc. Math. Stat. 313 (Springer, Cham, 2020), 7-20.

Last Updated September 2023