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The Probability Integral Its Origin, Its Importance, and Its Calculation

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, engineerin...

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Bibliographic Details
Main Author: Nahin, Paul J.
Format: eBook
Language:English
Published: Cham Springer Nature Switzerland 2023, 2023
Edition:1st ed. 2023
Subjects:
Measure Theory
Engineering Mathematics
History Of Statistics
Statistics 
Probability Theory
History
Mathematical Physics
Measure And Integration
Mathematics
Mathematical Methods In Physics
Probabilities
History Of Mathematical Sciences
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • 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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