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Scottish mathematician (1951–2016)
Jonathan Michael Borwein (20 May 1951 – 2 August 2016) was a Scottish mathematician who held an appointment as Laureate Professor of mathematics at the
Jonathan_Borwein
Surname list
Borwein is a surname. Notable people with the surname include: David Borwein (1924–2021), Lithuania-born Canadian mathematician Jonathan Borwein (1951–2016)
Borwein
Type of mathematical integrals
Borwein integral is an integral whose unusual properties were first presented by mathematicians David Borwein and Jonathan Borwein in 2001. Borwein integrals
Borwein_integral
Canadian mathematician (1953–2020)
Peter Benjamin Borwein (born St. Andrews, Scotland, May 10, 1953 – 23 August 2020) was a Canadian mathematician and a professor at Simon Fraser University
Peter_Borwein
Canadian mathematician (1924–2021)
David Borwein (March 24, 1924 – September 3, 2021) was a Lithuanian-born Canadian mathematician, known for his research in the summability theory of series
David_Borwein
Sum of the reciprocal of the Mersenne numbers
The Erdős–Borwein constant, named after Paul Erdős and Peter Borwein, is the sum of the reciprocals of the Mersenne numbers. By definition it is: E = ∑
Erdős–Borwein_constant
Mathematical optimization method
The Barzilai–Borwein method is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear
Barzilai–Borwein_method
Number, approximately 3.14
p. 342. doi:10.1511/2014.110.342. Retrieved 22 January 2022. Borwein, J. M.; Borwein, P. B. (1988). "Ramanujan and Pi". Scientific American. 256 (2):
Pi
Formula for computing the nth base-16 digit of π
The Bailey–Borwein–Plouffe formula (BBP formula) is a formula for π. It was discovered in 1995 by Simon Plouffe and is named after the authors of the
Bailey–Borwein–Plouffe formula
Bailey–Borwein–Plouffe_formula
Method for calculating the value of pi
Borwein's algorithm was devised by Jonathan and Peter Borwein to calculate the value of 1 / π {\displaystyle 1/\pi } . This and other algorithms can be
Borwein's_algorithm
American mathematician (born 1948)
Borwein and Simon Plouffe) of a 1997 paper that presented a new formula for π (pi), which had been discovered by Plouffe in 1995. This Bailey–Borwein–Plouffe
David H. Bailey (mathematician)
David_H._Bailey_(mathematician)
Approach to mathematics using computation
Wayback Machine by David H. Bailey, Jonathan M. Borwein, Peter B. Borwein and Simon Plouffe. Borwein, Jonathan; Bailey, David (2004). Mathematics by Experiment:
Experimental_mathematics
Conjecture on zeros of the zeta function
original (PDF) on 2015-12-22, retrieved 2008-10-25 Reprinted in (Borwein et al. 2008). Borwein, Peter; Choi, Stephen; Rooney, Brendan; Weirathmueller, Andrea
Riemann_hypothesis
Algorithmic runtime requirements for common math procedures
{\displaystyle n} . Many of the methods in this section are given in Borwein & Borwein. The elementary functions are constructed by composing arithmetic
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Mathematical formula
discovered by Fabrice Bellard in 1997. It is about 43% faster than the Bailey–Borwein–Plouffe formula (discovered in 1995). It has been used in PiHex, the now-completed
Bellard's_formula
Numerical utility
number checker established July 18, 1995 by Peter Benjamin Borwein, Jonathan Michael Borwein and Simon Plouffe of the Canadian Centre for Experimental
Inverse_Symbolic_Calculator
Function in analytic number theory
Note that the second, inside summation is a forward difference. Peter Borwein used approximations involving Chebyshev polynomials to produce a method
Dirichlet_eta_function
History of pi Approximations of pi David H. Bailey; Jonathan M. Borwein; Peter B. Borwein; Simon Plouffe (1997). "The quest for pi" (PDF). Mathematical
Chronology of computation of pi
Chronology_of_computation_of_pi
Imperial dynasty in China (202 BC – 220 AD)
Liu et al. (2003), pp. 9–10. Needham (1986a), pp. 99–100. Berggren, Borwein & Borwein (2004), p. 27. Dauben (2007), pp. 219–222. Needham (1986a), p. 22
Han_dynasty
Varying methods used to calculate pi
like the Gauss–Legendre algorithm and Borwein's algorithm. The latter, found in 1985 by Jonathan and Peter Borwein, converges extremely quickly: For y 0
Approximations_of_pi
Numbers obtained by adding the two previous ones
Soc. Math. France (in French), 27: 298–300, quoted accordingly in Borwein & Borwein (1998), p. 95, exercise 3b. Sloane, N. J. A. (ed.), "Sequence A079586
Fibonacci_sequence
Extension of the factorial function
doi:10.1023/A:1015706300169. S2CID 128246166. Bailey, David H.; Borwein, David; Borwein, Jonathan M. (2015). "On Eulerian log-gamma integrals and Tornheim-Witten
Gamma_function
Number theory conjecture
that if such a number exists, it has at least 13,800 digits (Borwein, Borwein, Borwein, Girgensohn 1996). Laerte Sorini, in a work of 2001 showed that
Agoh–Giuga_conjecture
Problem of constructing equal-area shapes
Houghton Mifflin Company. Retrieved 16 April 2012. Bailey, D. H.; Borwein, J. M.; Borwein, P. B.; Plouffe, S. (1997). "The quest for pi". The Mathematical
Squaring_the_circle
(Straffin 1998, p. 164) (Needham & Wang 1995, pp. 99–100) (Berggren, Borwein & Borwein 2004, p. 27) (de Crespigny 2007, p. 1050) (Boyer 1991, "China and
History_of_mathematics
Difference between logarithm and harmonic series
Masser-Gramain constant to four decimal digits" (PDF). Retrieved 2024-10-03. Borwein, Jonathan M.; David M. Bradley; Richard E. Crandall (2000). "Computational
Euler's_constant
Francisco J. Aragón Artacho; David H. Baileyy; Jonathan M. Borweinz; Peter B. Borwein (2012). Tools for visualizing real numbers (PDF). p. 33. Archived from
List of mathematical constants
List_of_mathematical_constants
Optimization algorithm
{x} _{n})-\nabla f(\mathbf {x} _{n-1})\right\|^{2}}}} as in the Barzilai-Borwein method, or a sequence η n {\displaystyle \eta _{n}} satisfying the Wolfe
Gradient_descent
Sum of a number's digits
by OEIS: A007953 in the On-Line Encyclopedia of Integer Sequences. Borwein & Borwein (1992) use the generating function of this integer sequence (and of
Digit_sum
State of being real
Chihara 1990, p. 3 Lucas 1990, p. 75 Vinogradov & Karatsuba 1986, p. 8 Borwein et al. 2008, p. 63 Lucas 1990, p. 75 Azzouni 2015, p. 133 Chihara 1990
Existence
Fixed number that has received a name
lemniscate or use different alphabets such as Hebrew, Cyrillic or Gothic. Erdős–Borwein constant E B {\displaystyle E_{B}} Embree–Trefethen constant β ∗ {\displaystyle
Mathematical_constant
Irrational algebraic number
9789004156050.i-1311. ISBN 9789047411840. Berggren, Lennart; Borwein, Jonathan; Borwein, Peter (2004). Pi: A Source Book. doi:10.1007/978-1-4757-4217-6
Square_root_of_10
Series related to Ramanujan's pi formulas
Computer Science Department, University of Illinois, hdl:2142/28348. Borwein, J. M.; Borwein, P. B.; Bailey, D. H. (1989). "Ramanujan, modular equations, and
Ramanujan–Sato_series
Mathematical constant
{1}{8k+4}}+{\frac {1}{16k+12}}\right){\frac {1}{16^{k}}}.} (See more about Bailey–Borwein–Plouffe (BBP)-type representations.) Applying the three general series
Natural_logarithm_of_2
Online database of integer sequences
22 June 2024. Sloane, Neil (2024). "The Email Servers and Superseeker". Borwein, Jonathan M. (2017). "Adventures with the OEIS". In Andrews, George E.;
On-Line Encyclopedia of Integer Sequences
On-Line_Encyclopedia_of_Integer_Sequences
Canadian mathematician
(born June 11, 1956) is a Canadian mathematician who discovered the Bailey–Borwein–Plouffe formula (BBP algorithm) which permits the computation of the nth
Simon_Plouffe
Existence of a line through two points
line can be found as a line of slope closest to zero; for details, see Borwein & Moser (1990). The 1941 proof by Melchior uses projective duality to convert
Sylvester–Gallai_theorem
Number divisible only by 1 and itself
Sandifer 2007, pp. 191–193. Borwein et al. 2008, Conjecture 2.7 (the Riemann hypothesis), p. 15. Patterson 1988, p. 7. Borwein et al. 2008, p. 18. Nathanson
Prime_number
Logarithm to the base of the mathematical constant e
302–312. doi:10.1007/3-540-49116-3_28. ISBN 978-3-540-65691-3. Borwein, Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number
Natural_logarithm
Quickly converging computation of π
the first 200 billion decimal digits of π, with results checked using Borwein's algorithm. Initial value setting: a 0 = 1 b 0 = 1 2 p 0 = 1 t 0 = 1 4
Gauss–Legendre_algorithm
Constant in crystallography
although very slowly. An alternative summation procedure, presented by Borwein, Borwein and Taylor, uses analytic continuation of an absolutely convergent
Madelung_constant
1897 proposed law to define squaring the circle
2307/2971093. JSTOR 2971093. Reprinted in: Lennart Berggren, Jonathan Borwein, and Peter Borwein, Pi: A Source Book, 3rd ed. (New York, New York: Springer-Verlag
Indiana_pi_bill
Fast method for calculating the digits of π
computations is called binary splitting. Mathematics portal Bailey–Borwein–Plouffe formula Borwein's algorithm Approximations of π Chudnovsky, David; Chudnovsky
Chudnovsky_algorithm
Base-16 numeric representation
respectively Complexity of accepting both upper and lower case letters Bailey–Borwein–Plouffe formula – Formula for computing the nth base-16 digit of π Hex
Hexadecimal
Chinese scientist and statesman (78–139)
Berggren, Borwein & Borwein 2004, p. 27 Arndt & Haenel 2001, p. 177 Wilson 2001, p. 16 Needham 1986, pp. 100–101 Berggren, Borwein & Borwein 2004, pp. 20
Zhang_Heng
Mathematical function of two positive real arguments
and Synthesis. Springer. pp. 147–155. ISBN 978-94-007-2189-0. Borwein, Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number
Arithmetic–geometric_mean
a small perturbation to the function. A smooth variant is known as the Borwein-Press variational principle. The classical Fermat's theorem says that if
Variational_analysis
Special mathematical function defined as sin(x)/x
1980. doi:10.1080/00029890.1980.11995075. Robert Baillie; David Borwein; Jonathan M. Borwein (December 2008). "Surprising Sinc Sums and Integrals". American
Sinc_function
French computer programmer
representation, known as Bellard's formula. It is a variant of the Bailey–Borwein–Plouffe formula. Bellard's entries won the International Obfuscated C Code
Fabrice_Bellard
Special function defined by an integral
analytically extended to the complex plane. Carlson 2010, 19.8. Borwein, Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number
Elliptic_integral
Special mathematical function
higher integer orders (Lewin 1991, p. 2), but one has for instance (Borwein, Borwein & Girgensohn 1995): Li 4 ( 1 2 ) = 1 360 π 4 − 1 24 ( ln 2 ) 4
Polylogarithm
Fourth letter in the Greek alphabet
of sets A and B is variously written as A ⊖ B, A∇ B, A+B (Borowski and Borwein 1991) or AΔB (Harris and Stocker 1998, p. 3). All but the first notation
Delta_(letter)
Mathematical constant in number theory
Lévy's constant Somos' constant List of mathematical constants Bailey, Borwein & Crandall, 1997. In that paper, a slightly non-standard definition is
Khinchin's_constant
Jain cosmological text
(1962) Ac 6785. Digital Library Of India. pp. 22–25. Bailey, David H.; Borwein, Jonathan M.; Mattingly, Andrew; Wightwick, Glenn (1 August 2013). "The
Lokavibhaga
Canadian mathematician
inaugural class of fellows. In 2022 was the recipient of the 2022 David Borwein Distinguished Career Award by the Canadian Mathematical Society (CMS),
Jacques Hurtubise (mathematician)
Jacques_Hurtubise_(mathematician)
von (2004) [1882], "Ueber die Zahl π", in Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (eds.), Pi, a source book (3rd ed.), New York: Springer-Verlag
Proof_that_pi_is_irrational
Mathematical procedure
the PSLQ algorithm to find the integer relation that led to the Bailey–Borwein–Plouffe formula for the value of π. PSLQ has also helped find new identities
Integer_relation_algorithm
Signed odd unit fractions sum to π/4
technique that can be applied to the Leibniz series. In 1992, Jonathan Borwein and Mark Limber used the first thousand Euler numbers to calculate π to
Leibniz_formula_for_π
Unsolved problem in number theory
Hardy–Littlewood circle method and his polynomial concentration results. In 2006, Borwein, Choi, and Chu proved that for all additive bases B {\displaystyle B}
Erdős–Turán conjecture on additive bases
Erdős–Turán_conjecture_on_additive_bases
Analytic function in mathematics
{O}}\left(k^{-3/4+\varepsilon }\right)\qquad (\forall \varepsilon >0)} Peter Borwein developed an algorithm that applies Chebyshev polynomials to the Dirichlet
Riemann_zeta_function
Mathematics reference book (2008)
interest even professional research mathematicians. Reviewer Jonathan Borwein summarizes the audience for this book broadly: Every research mathematician
The Princeton Companion to Mathematics
The_Princeton_Companion_to_Mathematics
series" (PDF), J. Indian Math. Soc., New Series, 12: 63–66, MR 0029405 Borwein, Peter B. (1992), "On the irrationality of certain series", Mathematical
List_of_numbers
Approximations of π Arithmetic–geometric mean Bailey–Borwein–Plouffe formula Basel problem Borwein's algorithm Buffon's needle Cadaeic Cadenza Chronology
List_of_topics_related_to_π
Species of fungus
plant pathogen. Diaporthe arctii var. achilleae Bailey, David H.; Borwein, Peter; Borwein, Jonathan M. (2023), "Annotated notes on Diaporthe species" (PDF)
Diaporthe_arctii
Canadian computer scientist (born 1980)
officially enrolled at SFU in 1998. At SFU he studied number theory under Peter Borwein, and competed in the William Lowell Putnam Mathematical Competition, placing
Colin_Percival
German-Dutch mathematician
America". www.maa.org. Retrieved 2022-12-31. Berggren, J. L.; Borwein, Jonathan; Borwein, Peter (2014). Pi: A Source Book (Third ed.). New York: Springer
Ludolph_van_Ceulen
Transcendental single-variable function
the types of resummation techniques used to obtain rational zeta series (Borwein et al. 2000). Recall the Barnes G-function, the Catalan's constant K and
Clausen_function
Identity expressing an integral as a sum
log 1 = 0. Bernoulli, Johann (1697). Opera omnia. Vol. 3. pp. 376–381. Borwein, Jonathan; Bailey, David H.; Girgensohn, Roland (2004). Experimentation
Sophomore's_dream
Prime number of the form 2^n – 1
(sequence A222119 in the OEIS) Repunit Fermat number Power of two Erdős–Borwein constant Mersenne conjectures Mersenne twister Double Mersenne number Prime95
Mersenne_prime
Functions of an angle
transcendantes circulaires et logarithmiques", in Berggren, Lennart; Borwein, Jonathan M.; Borwein, Peter B. (eds.), Pi, a source book (3rd ed.), New York: Springer-Verlag
Trigonometric_functions
Mathematical power series of arctangent
Civilisation. p. 231. ISBN 978-81-317-0871-2. Berggren, Lennart; Borwein, Jonathan; Borwein, Peter, eds. (2004). Pi: A Source Book (3rd ed.). Springer. doi:10
Arctangent_series
Canadian mathematician
manifolds and computation of invariants. His doctoral students include Peter Borwein. Killam Senior Research Fellowship, 1976–77 and 1981–82 Steacie Prize,
David_William_Boyd
Award for expository papers in mathematics
King 1995: Andrew Granville 1993: David H. Bailey, Jonathan M. Borwein, and Peter B. Borwein 1991: Barry Arthur Cipra 1989: Irl Bivens 1987: Anthony Barcellos
Merten_M._Hasse_Prize
Numerical integration method
schemes". Experimental Mathematics, 14.3 (2005). Bailey, David H, Jonathan M. Borwein, David Broadhurst, and Wadim Zudlin, Experimental mathematics and mathematical
Tanh-sinh_quadrature
Mathematical formula involving a given set of operations
440–448, arXiv:math/9805045, doi:10.2307/2589148, JSTOR 2589148 Jonathan M. Borwein and Richard E. Crandall (January 2013), "Closed Forms: What They Are and
Closed-form_expression
Coincidence in mathematics
Line 47 Weisstein, Eric W. "Almost Integer". MathWorld. Bailey, David; Borwein, Jonathan; Kapoor, Vishal; Weisstein, Eric (9 March 2006). "Ten Problems
Mathematical_coincidence
Erdős and Peter Borwein Eddington number – Arthur Stanley Eddington Dunbar's number – Robin Dunbar Embree–Trefethen constant Erdős–Borwein constant Euler–Mascheroni
List of scientific constants named after people
List_of_scientific_constants_named_after_people
Surname list
Plouffe Family (film) (French: Les Plouffe), 1981 Canadian drama film Bailey–Borwein–Plouffe formula, a formula for computing π The Crime of Ovide Plouffe (French:
Plouffe
Professor of statistics
Scientific Computing: Principles and Practice," David H. Bailey, Jonathan M. Borwein and Victoria Stodden, in Harald Atmanspacher and Sabine Maasen, eds, Reproducibility:
Victoria_Stodden
Algorithms for calculating square roots
Johnson 2015. Nemiroff & Bonnell 1994. Nemiroff & Bonnell 1994a. Bailey & Borwein 2012. Simply Curious 2018. Herrero Piñeyro, P. J.; Linero Bas, A.; Massa
Square_root_algorithms
Mathematical expression
"An alternative way to calculate $\log(x)$". Mathematics Stack Exchange. Borwein, Crandall & Fee 2004, p. 278, 280. Beckmann 1971. Angell, David (2010)
Continued_fraction
Exploring properties of the integers with complex analysis
2013, at the Wayback Machine (with English translation). Reprinted in (Borwein et al. 2008) and (Edwards 1974) Ingham, A.E. (1990). The Distribution of
Analytic_number_theory
Algorithmic technique
number-theoretic constants. Info. Proc. Letters, N 62, pp. 145–152 (1997). Borwein, J.M., Bradley, D.M. and Crandall, R.E. Computational strategies for the
Binary_splitting
Hitchin (Savilian Professor of Geometry at Oxford 1997–2016), Jonathan Borwein (a former Rhodes Scholar who has held professorial appointments in Canada
List of mathematicians, physicians, and scientists educated at Jesus College, Oxford
List_of_mathematicians,_physicians,_and_scientists_educated_at_Jesus_College,_Oxford
Summation method for some divergent series
h\in [0,1]} and f ( k ) {\displaystyle f^{(k)}} is the kth derivative. Borwein, Jonathan M.; Calkin, Neil J.; Manna, Dante (2009), "Euler–Boole summation
Euler–Boole_summation
Publisher of scientific and technical books
publisher by Taylor & Francis. A K Peters, with the participation of Jonathan Borwein, published as books three collective works on experimental mathematics:
A_K_Peters
Disproved mathematical conjecture
O ( x 1 2 ) . {\displaystyle M(x)=O{\Big (}x^{\tfrac {1}{2}}{\Big )}.} Borwein, Peter; Choi, Stephen; Rooney, Brendan; Weirathmueller, Andrea, eds. (2007)
Mertens_conjecture
Japanese mathematician (1949–2020)
supercomputer. Some of his competitors in recent years include Jonathan and Peter Borwein and the Chudnovsky brothers. Chronology of computation of π Mcavoy, Audrey
Yasumasa_Kanada
Mathematical constants
\Gamma \left({\tfrac {1}{4}}\right)={\sqrt {2\varpi {\sqrt {2\pi }}}}} Borwein and Zucker have found that Γ(n/24) can be expressed algebraically in
Particular values of the gamma function
Particular_values_of_the_gamma_function
Uses of the constant
Pi. American Mathematical Society. ISBN 0-8218-3246-8. p. 2 Borwein, Jonathan M.; Borwein, Peter B. (1987). Pi and the AGM: A Study in Analytic Number
List_of_formulae_involving_π
Inverse functions of sin, cos, tan, etc.
p. 64. ISBN 978-1-337-61392-7. Abramowitz & Stegun 1972, p. 73, 4.3.44 Borwein, Jonathan; Bailey, David; Gingersohn, Roland (2004). Experimentation in
Inverse trigonometric functions
Inverse_trigonometric_functions
24–26. Berggren, Borwein & Borwein (2004), 26. Berggren, Borwein & Borwein (2004), 20. Gupta (1975), B45–B48 Berggren, Borwein, & Borwein (2004), 24. Sivin
List_of_Chinese_discoveries
Akeel Bilgrami University of Mumbai Balliol 1971 India Philosopher Jon Borwein University of Western Ontario Jesus 1971 Canada Experimental mathematics
List_of_Rhodes_Scholars
Set of points equidistant from a center
Central". mathcentral.uregina.ca. Retrieved 10 June 2019. E.J. Borowski; J.M. Borwein (1989). Collins Dictionary of Mathematics. Collins. pp. 141, 149. ISBN 978-0-00-434347-1
Sphere
is now referred to as the Borwein–Erdélyi inequality. He is also known for establishing the full Müntz theorem with Borwein and Johnson, and has some
Tamás_Erdélyi_(mathematician)
Testing a predictive model on historical data
potential loss for an investment under a given set of conditions Bailey, Borwein, Lopez de Prado, Zhu (2014). "Pseudo-mathematics and financial charlatanism
Backtesting
Infinite product converging to 2/π
formula as marking the beginning of mathematical analysis and Jonathan Borwein calls its appearance "the dawn of modern mathematics". Using his formula
Viète's_formula
Inverse of the gamma function
( n ) ( x ) {\displaystyle \psi ^{(n)}(x)} is the polygamma function. Borwein, Jonathan M.; Corless, Robert M. (2017). "Gamma and Factorial in the Monthly"
Inverse_gamma_function
American politician David Borthwick (born 1962), Scottish shinty player David Borwein (1924–2021), Canadian mathematician David Bossie (born 1965), American
List of people with given name David
List_of_people_with_given_name_David
Mathematical functions that quantify complexity
66–67) Lang (1988, pp. 156–157) Fili, Petsche, and Pritsker (2017, p. 441) Borwein (2002) Mahler (1963) Bump (1998) Kolmogorov and Fomin (1957, p. 5) Baker
Height_function
BORWEIN
BORWEIN
BORWEIN
BORWEIN
Boy/Male
Tamil
To regin universally
Girl/Female
Muslim/Islamic
One with round face
Boy/Male
Hindu
Polish
Boy/Male
Muslim
With God, Lord Buddha, Chief of army
Boy/Male
Tamil
Lohitaksh | லோஹீதகà¯à®·à®¾Â
Lord Vishnu
Boy/Male
Tamil
The one who brings hope
Girl/Female
Australian, Hebrew
The Lord is Good
Surname or Lastname
English
English : variant of Ellison.
Boy/Male
Tamil
Help, Lord Shiva
Boy/Male
American, Australian, British, English, Greek
Son of Dennis; Dennis' Son
BORWEIN
BORWEIN
BORWEIN
BORWEIN
BORWEIN