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A compendium of BBPtype formulas for mathematical constants
, 2000
"... A 1996 paper by the author, Peter Borwein and Simon Plouffe showed that any mathematical constant given by an infinite series of a certain type has the property that its nth digit in a particular number base could be calculated directly, without needing to compute any of the first n−1 digits, by me ..."
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A 1996 paper by the author, Peter Borwein and Simon Plouffe showed that any mathematical constant given by an infinite series of a certain type has the property that its nth digit in a particular number base could be calculated directly, without needing to compute any of the first n−1 digits, by means of a simple algorithm that does not require multipleprecision arithmetic. Several such formulas were presented in that paper, including formulas for the constants π and log 2. Since then, numerous other formulas of this type have been found. This paper presents a compendium of currently known results of this sort, both formal and experimental. Many of these results were found in the process of compiling this collection and have not previously appeared in the literature. Several conjectures suggested by these results are mentioned.
Binary BBPformulae for logarithms and generalized Gaussian–Mersenne primes
 MR2046407 (2005a:11201), Zbl 1073.11076
"... Constants of the form ..."
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Preface
"... This document is an adapted selection of excerpts from two newly published books, Mathematics by Experiment: Plausible Reasoning in the 21st Century, and Experimentation in Mathematics: Computational Paths to Discovery, published ..."
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This document is an adapted selection of excerpts from two newly published books, Mathematics by Experiment: Plausible Reasoning in the 21st Century, and Experimentation in Mathematics: Computational Paths to Discovery, published
Experimental Mathematics and Computational Statistics
, 2009
"... The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of “experimental mathematics.” These includes both applications of experimental mathematics in statistics ..."
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The field of statistics has long been noted for techniques to detect patterns and regularities in numerical data. In this article we explore connections between statistics and the emerging field of “experimental mathematics.” These includes both applications of experimental mathematics in statistics, as well as statistical methods applied to computational mathematics.
The Computation of Previously Inaccessible Digits of π 2 and Catalan’s Constant
, 2011
"... The admirable number pi: three point one four one. All the following digits are also initial, ..."
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The admirable number pi: three point one four one. All the following digits are also initial,
A Pamphlet on Pi (serving as a supplement to . . .
, 2003
"... Our aim in preparing this pamphlet is to bring the material in the collection of papers in the second edition of our Pi: A Source Book [9] up to date. Moreover, several delightful pieces came available and are added. This substantial supplement to the third addition serves as a stand alone expositio ..."
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Our aim in preparing this pamphlet is to bring the material in the collection of papers in the second edition of our Pi: A Source Book [9] up to date. Moreover, several delightful pieces came available and are added. This substantial supplement to the third addition serves as a stand alone exposition of the recent history of the computation of digits of Pi. It also includes a discussion of the thorny old question of normality of the distribution of the digits. Additional material of historical and cultural interest is included, the most notable being new translations of the two Latin pieces of Viète (Translation
Using Integer Relations Algorithms for Finding . . .
, 2007
"... Nearly three decades ago the first integer relations algorithm was developed. Given a set of numbers {x1,..., xm}, an integer relations algorithm seeks integers {a1,..., am} such that a1x1+ · · ·+amxm = 0. One of the most popular and efficient of these is the PSLQ algorithm, listed as one of the to ..."
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Nearly three decades ago the first integer relations algorithm was developed. Given a set of numbers {x1,..., xm}, an integer relations algorithm seeks integers {a1,..., am} such that a1x1+ · · ·+amxm = 0. One of the most popular and efficient of these is the PSLQ algorithm, listed as one of the top ten algorithms of the 20th century[2]. This algorithm either finds the integers or obtains lower bounds on the sizes of coefficients for which such a relation will hold. PSLQ has been implemented in both Maple and Mathematica. Typically a high degree of numerical precision is needed for PSLQ to run effectively. If the precison is not sufficiently high, “large” coefficients are produced suggesting a relation has not been found. PSLQ has been used to find relationships between various constants. Its first wellknown success was in finding the formula π = k=0