• Abdul J. Jerri
Part of the Mathematics and Its Applications book series (MAIA, volume 446)


We should mention at the outset that the well-known Gibbs phenomenon was first discovered analytically by Henry Wilbraham [1] in 1848. This was a half century before the famous mathematical physicist Josiah W. Gibbs [2,3] explained its presence in the output of the supposedly extremely accurate harmonic analyzer of Albert A. Michelson and S.W. Stratton in 1898 [4] (see also Michelson [5], [6]). As we elaborate on the historical development in Section 2.7, it seems that the results of Wilbraham were almost forgotten for about eighty years until Carslaw [7] brought it to some light in his short historical note in 1925 (see also Carslaw [8], [9]). This raises the legitimate question of whether the phenomenon should be re-named as “Gibbs-Wilbraham Phenomenon?”. Such a question of credit and priority may be still a subject of discussion among the concerned researchers. In the meantime, and for using the name familiar to most, we shall use “The Gibbs Phenomenon”; besides telling the story that recognizes Wilbraham’s effort, which is long overdue. Fortunately, this story is well told by E. Hewitt and R. Hewitt [10] in 1980.


Fourier Series Jump Discontinuity Convolution Product Convolution Theorem Gibbs Phenomenon 
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  1. 2.
    R. V. Churchill, Operational Mathematics, McGraw Hill, New York, 1972, p. 393.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1998

Authors and Affiliations

  • Abdul J. Jerri
    • 1
  1. 1.Department of Mathematics and Computer ScienceClarkson UniversityPotsdamUSA

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