Gibbs Phenomenon/Historical Note
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Historical Note on Gibbs Phenomenon
The Gibbs phenomenon was first reported in print in $1848$ by Henry Wilbraham.
However, this went unnoticed at the time.
Josiah Willard Gibbs published a short note in $1899$ on the subject of the Fourier series of a square wave, but failed to report on the phenomenon at that time.
Later that year he published a correction to that note in which the overshoot was described accurately.
In $1906$ Maxime Bôcher gave a complete analysis of the mathematics behind the phenomenon, and called it the Gibbs Phenomenon.
Wilbraham's paper was later brought to light, but by that time it was generally attributed to Gibbs.
In the words of Horatio Scott Carslaw ($1925$):
- We may still call this property of Fourier's series (and certain other series) Gibbs's phenomenon; but we must no longer claim that the property was first discovered by Gibbs.
Sources
- 1848: Henry Wilbraham: On a certain periodic function (The Cambridge and Dublin Mathematical Journal Vol. 3: pp. 198 – 201)
- 1899: J. Willard Gibbs: Fourier Series (Nature Vol. 59: p. 200)
- 1899: J. Willard Gibbs: Fourier Series (Nature Vol. 59: p. 606)
- 1906: Maxime Bôcher: Introduction to the theory of Fourier's series (Ann. Math. Vol. 7: pp. 81 – 152) www.jstor.org/stable/1967238
- 1914: Maxime Bôcher: On Gibbs's Phenomenon (J. reine angew. Math. Vol. 144: pp. 41 – 47)
- 1925: H.S. Carslaw: A historical note on Gibbs' phenomenon in Fourier's series and integrals (Bull. Amer. Math. Soc. Vol. 31: pp. 420 – 424)