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The Value of Zeta(3) to 1,000,000 places   By: (1956-)

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In "The Value of Zeta(3) to 1,000,000 Places," Simon Plouffe delves into the fascinating and complex world of mathematics to explore the enigmatic value of Zeta(3) (also known as Apéry's constant) with remarkable depth and precision. Plouffe's book is a comprehensive exploration of a specific mathematical constant and its implications, a subject that may intimidate some readers but also promises endless rewards for those with a genuine interest in the field.

Plouffe begins by laying a solid foundation for readers unfamiliar with the concept of Zeta(3). He introduces the concept of Riemann's zeta function and its significance in mathematics, gradually guiding readers from the basics to the more intricate aspects of this constant. This step-by-step approach allows both novices and experienced mathematicians to appreciate the depth and profound implications of Zeta(3).

The author's writing style is both informative and engaging, striking an excellent balance between technicality and accessibility. He uses clear and concise language that effectively conveys complex mathematical concepts, making the subject matter digestible, even for readers who may not possess a strong mathematical background. Plouffe's passion for the subject shines through, fostering a sense of curiosity and fascination in the readers' minds as they follow him on this mathematical journey.

One of the most impressive aspects of Plouffe's work is his dedication to precision and accuracy. As the title suggests, he goes above and beyond in providing the value of Zeta(3) to an astonishing 1,000,000 decimal places. While this level of detail may not be essential to all readers, it showcases the author's commitment to thoroughness and meticulousness. It also serves as a testament to the significance of precision in mathematics and its implications for the broader field.

Another noteworthy feature of "The Value of Zeta(3) to 1,000,000 Places" is the inclusion of a variety of applications and connections to related fields of mathematics. Plouffe skillfully demonstrates the relevance of Zeta(3) in various mathematical problems, highlighting its presence in areas such as number theory, combinatorics, and calculus. This comprehensive approach enriches the reading experience and allows readers to gain a deeper appreciation for the real-world implications and applications of this seemingly abstract mathematical value.

While "The Value of Zeta(3) to 1,000,000 Places" is undeniably a niche book that caters primarily to mathematicians, it possesses a broader appeal due to the author's talent in explaining complex mathematical principles in an accessible manner. Plouffe seamlessly guides readers through the intricacies of Zeta(3), unraveling its mysteries and making it an engaging subject for mathematicians, enthusiasts, and curious minds alike.

In conclusion, "The Value of Zeta(3) to 1,000,000 Places" is a remarkable mathematical journey that explores the significance and intricacies of a specific mathematical constant. Simon Plouffe's passion for the subject shines through in his engaging writing style and meticulous attention to detail. Whether you're a mathematician looking to explore a fascinating constant or a curious reader seeking to delve into the realm of mathematics, this book provides a comprehensive and rewarding exploration of Zeta(3) and its profound implications for the broader field.

First Page:

Mathematical constants and numbers edited by Simon Plouffe Associate Professor LaCIM, University of Quebec at Montreal http://www.lacim.uqam.ca/pi : Plouffe's Inverter plouffe@math.uqam.ca

The value of Zeta(3) to 1,000,000 decimal digits. the number is defined as sum(1/n^3,n=1..infinity), the sum of inverses of cubes and equals 1.2020569031...

Computed by : Sebastian Wedeniwski (wedeniws@de.ibm.com) who computed more than 128 million digits using this more efficient formula found by Theodor Amdeberhan and Doron Zeilberger.

/ \ 3 \ n A(n) ((2 n 1)! (2 n)! n!) Zeta(3) = 1/24 ) ( 1) / 3 (3 n 2)! ((4 n 3)!) \ n >= 0 /

5 4 3 2 with A(n) := 126392 n 412708 n 531578 n 336367 n 104000 n 12463 given by Theodor Amdeberhan and Doron Zeilberger (see [1]).

References: ===========

[1] T. Amdeberhan und D. Zeilberger: Hypergeometric Series Acceleration via the WZ Method, Electronic Journal of Combinatorics (Wilf Festschrift Volume) 4 (1997)... Continue reading book >>




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