The probability integral : its origin, its importance, and its calculation / Paul J. Nahin.
Nahin, Paul J., author.
2023
QA273
Available Online

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Title The probability integral : its origin, its importance, and its calculation / Paul J. Nahin.
Author Nahin, Paul J., author.
ISBN 9783031384165 (electronic bk.)
3031384164 (electronic bk.)
9783031384158
3031384156
DOI https://doi.org/10.1007/978-3-031-38416-5
Published Cham : Springer, 2023.
Language English
Description 1 online resource (xxx, 189 pages) : color illustrations
Other Standard Identifiers 10.1007/978-3-031-38416-5 doi
Call Number QA273
Dewey Decimal Classification 519.2
Summary This book tells the story of the probability integral, the approaches to analyzing it throughout history, and the many areas of science where it arises. The so-called probability integral, the integral over the real line of a Gaussian function, occurs ubiquitously in mathematics, physics, engineering and probability theory. Stubbornly resistant to the undergraduate toolkit for handling integrals, calculating its value and investigating its properties occupied such mathematical luminaries as De Moivre, Laplace, Poisson, and Liouville. This book introduces the probability integral, puts it into a historical context, and describes the different approaches throughout history to evaluate and analyze it. The author also takes entertaining diversions into areas of math, science, and engineering where the probability integral arises: as well as being indispensable to probability theory and statistics, it also shows up naturally in thermodynamics and signal processing. Designed to be accessible to anyone at the undergraduate level and above, this book will appeal to anyone interested in integration techniques, as well as historians of math, science, and statistics.
Note Includes index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed September 19, 2023).
Available in Other Form The Probability Integral
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Chapter 1. De Moivre and the Discovery of the Probability Integral
Chapter 2. Laplace's First Derivation
Chapter 3. How Euler Could Have Done It Before Laplace (but did he?)
Chapter 4. Laplace's Second Derivation
Chapter 5. Generalizing the Probability Integral
Chapter 6. Poisson’s Derivation
Chapter 7. Rice's Radar Integral
Chapter 8. Liouville’s Theorem that Has No Finite Form
Chapter 9. How the Error Function Appeared in the Electrical Response of the Trans-Atlantic Telegraph Cable
Chapter 10. Doing the Probability Integral with Differentiation
chapter 11. The Probability Integral as a Volume
Chapter 12. How Cauchy Could Have Done It (but didn't)
Chapter 13. Fourier Has the Penultimate Technical Word
Chapter 14. Finbarr Holland Has the Last Technical Word
Chapter 15. A Final Comment on Mathematical Proofs.

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