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Original Articles

On the Random Character of Fundamental Constant Expansions

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Pages 175-190 | Published online: 04 Apr 2012

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Read on this site (8)

Carlos Sevcik. (2018) Fractal Analysis of Pi Normality. Experimental Mathematics 27:3, pages 331-343.
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Quentin F. Gronau & Eric-Jan Wagenmakers. (2018) Bayesian Evidence Accumulation in Experimental Mathematics: A Case Study of Four Irrational Numbers. Experimental Mathematics 27:3, pages 277-286.
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David H. Bailey, Jonathan M. Borwein, Richard P. Brent & Mohsen Reisi. (2017) Reproducibility in Computational Science: A Case Study: Randomness of the Digits of Pi. Experimental Mathematics 26:3, pages 298-305.
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David H. Bailey, Jonathan M. Borwein, Vishaal Kapoor & Eric W. Weisstein. (2006) Ten Problems in Experimental Mathematics. The American Mathematical Monthly 113:6, pages 481-509.
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Hei-Chi Chan. (2006) More Formulas for π. The American Mathematical Monthly 113:5, pages 452-455.
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DavidH. Bailey & RichardE. Crandall. (2002) Random Generators and Normal Numbers. Experimental Mathematics 11:4, pages 527-546.
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JeffreyC. Lagarias. (2001) On the Normality of Arithmetical Constants. Experimental Mathematics 10:3, pages 355-368.
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Articles from other publishers (27)

Daisuke Takahashi. (2021) On the use of Montgomery multiplication in the computation of binary BBP-type formulas for mathematical constants. The Ramanujan Journal 59:1, pages 211-219.
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Xin Wu, Zhongfan Chen & Yinan Zhu. (2022) New BBP-Type Formulae for π Derived from New Forms of Taylor Expansions of Inverse Tangent Function. Mathematics 10:3, pages 290.
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Fenglei Fan & Ge Wang. (2018) Learning From Pseudo-Randomness With an Artificial Neural Network–Does God Play Pseudo-Dice?. IEEE Access 6, pages 22987-22992.
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Konstantinos F. Xylogiannopoulos, Panagiotis Karampelas & Reda Alhajj. (2016) Repeated patterns detection in big data using classification and parallelism on LERP Reduced Suffix Arrays. Applied Intelligence 45:3, pages 567-597.
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David H. Bailey & Jonathan M. BorweinFrancisco J. Aragón Artacho, David H. Bailey, Jonathan M. Borwein & Peter B. Borwein. 2016. Pi: The Next Generation. Pi: The Next Generation 341 361 .
Jean-Marie De Koninck. 2015. Scalable Uncertainty Management. Scalable Uncertainty Management 3 18 .
Martin Quack. 2014. Proceedings of the 240 Conference. Proceedings of the 240 Conference 97 118 .
Philip J. Davis. (2014) The relevance of the irrelevant beginning. ScienceOpen Research 0:0.
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Kundle Adegoke. (2013) Formal proofs of degree 5 binary BBP-type formulas. Functiones et Approximatio Commentarii Mathematici 48:1.
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Francisco J. Aragón Artacho, David H. Bailey, Jonathan M. Borwein & Peter B. Borwein. (2012) Walking on Real Numbers. The Mathematical Intelligencer 35:1, pages 42-60.
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Yoshitsugu OonoYoshitsugu Oono. 2013. The Nonlinear World. The Nonlinear World 235 291 .
D.H. Bailey, R. Barrio & J.M. Borwein. (2012) High-precision computation: Mathematical physics and dynamics. Applied Mathematics and Computation 218:20, pages 10106-10121.
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Bernhard Fechner. (2011) 3,14159... oder die n?herungsweise Berechnung von ?. Informatik-Spektrum 35:3, pages 215-219.
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Kunle Adegoke. (2012) A Novel Approach to the Discovery of Binary BBP-Type Formulas for Polylogarithm Constants. Integers 12:3.
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Julien Barral & Patrick Loiseau. (2011) Large deviations for the local fluctuations of random walks. Stochastic Processes and their Applications 121:10, pages 2272-2302.
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David H. Bailey & Jonathan M. Borwein. (2009) Experimental mathematics and computational statistics. Wiley Interdisciplinary Reviews: Computational Statistics 1:1, pages 12-24.
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Jonathan Borwein & David Bailey. 2008. Mathematics by Experiment. Mathematics by Experiment 187 226 .
Hua Yang & Guo-Ping Jiang. (2008) Irrational-Based Time-Hopping Modulation for UWB Communications. IEEE Transactions on Circuits and Systems II: Express Briefs 55:4, pages 364-368.
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Johannes Buchmann, Richard Lindner & Markus Rückert. 2008. Post-Quantum Cryptography. Post-Quantum Cryptography 79 94 .
BORIS ADAMCZEWSKI & YANN BUGEAUD. (2007) Dynamics for β -shifts and Diophantine approximation . Ergodic Theory and Dynamical Systems 27:6, pages 1695-1711.
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D.H. Bailey. (2005) High-precision floating-point arithmetic in scientific computation. Computing in Science & Engineering 7:3, pages 54-61.
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SHU-JU TU & EPHRAIM FISCHBACH. (2011) A STUDY ON THE RANDOMNESS OF THE DIGITS OF π. International Journal of Modern Physics C 16:02, pages 281-294.
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J. M. Borwein & K. Karamanos. 2005. Generalized Convexity, Generalized Monotonicity and Applications. Generalized Convexity, Generalized Monotonicity and Applications 3 21 .
Jonathan M. Borwein, David Borwein & William F. Galway. (2018) Finding and Excluding b -ary Machin-Type Individual Digit Formulae . Canadian Journal of Mathematics 56:5, pages 897-925.
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D. Byatt, M.L. Dalrymple & R.M. Turner. (2004) Searching for primes in the digits of ?. Computers & Mathematics with Applications 48:3-4, pages 497-504.
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David Corfield. 2009. Towards a Philosophy of Real Mathematics. Towards a Philosophy of Real Mathematics.
D.H. Bailey, D. Broadhurst, Y. Hida, Xiaoye S. Li & B. Thompson. (2002) High Performance Computing Meets Experimental Mathematics. High Performance Computing Meets Experimental Mathematics.

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