Titlebook: Computational and Analytical Mathematics; In Honor of Jonathan David H. Bailey,Heinz H. Bauschke,Henry Wolkowicz Conference proceedings 201

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2194-1009 al mathematics.Includes supplementary material: .The research of Jonathan Borwein has had a profound impact on optimization, functional analysis, operations research, mathematical programming, number theory, and experimental mathematics. Having authored more than a dozen books and more than 300 publ

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,Symmetry and Attractors: The Case , ≤ 4,nn zeta function, in the case when the two arguments are positive integers with opposite parity. Here, we establish a .-analog of Euler’s evaluation. That is, we state and prove a 1-parameter generalization that reduces to Euler’s evaluation in the limit as the parameter . tends to 1.

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https://doi.org/10.1007/978-1-4614-0299-2(. .) integer operations. These algorithms are extremely simple and fast for moderate values of .. They are faster and use less space than the algorithms of Atkinson (for Tangent and Secant numbers) and Akiyama and Tanigawa (for Bernoulli numbers).

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https://doi.org/10.1007/978-3-7643-7555-3s arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove such identities for the root system G..

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,Champernowne’s Number, Strong Normality, and the X Chromosome,s new criterion “strong normality.” We show that almost all numbers are strongly normal and that strong normality implies normality. However, Champernowne’s number is not strongly normal. We adapt a method of Sierpiński to construct an example of a strongly normal number.

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Logarithmic and Complex Constant Term Identities,s arise naturally by differentiating as-yet-conjectural complex analogues of the constant term identities of Dyson and Morris. We also discuss the existence of complex and logarithmic constant term identities for arbitrary root systems, and in particular prove such identities for the root system G..