Source of Name
This entry was named for Josiah Willard Gibbs.
The Gibbs phenomenon was first reported in print in $1848$ by Henry Wilbraham.
However, this went unnoticed at the time.
Later that year he published a correction to that note in which the overshoot was described accurately.
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.
- 1899: J. Willard Gibbs: Fourier Series (Nature Vol. 59: 200)
- 1899: J. Willard Gibbs: Fourier Series (Nature Vol. 59: 606)
- 1983: François Le Lionnais and Jean Brette: Les Nombres Remarquables ... (previous) ... (next): $1,17897 97444 \ldots$
- Weisstein, Eric W. "Gibbs Phenomenon." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GibbsPhenomenon.html