# Fourier's Series

@article{GibbsFouriersS, title={Fourier's Series}, author={Josiah Willard Gibbs}, journal={Nature}, volume={59}, pages={200-200} }

I SHOULD like to add a few words concerning the subject of Prof. Michelson's letter in NATURE of October 6. In the only reply which I have seen (NATURE, October 13), the point of view of Prof. Michelson is hardly considered.

## 237 Citations

Differentiation of a Fourier series

- Mathematics
- 2018

It is very known that if the operator acts on each term into a convergent Fourier series (FS) then it may result a divergent series. This situation is remedied applying the symmetric derivative to…

The Centuries Before Computers

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- 2018

For a long time after the Greek era not much happened when it comes to computation. Certainly Chinese mathematicians were active. Some of them continued to compute π to higher accuracy, and in Sect.…

The Gibbs phenomenon for piecewise-linear approximation

- Mathematics
- 1991

In 1899 J. W. Gibbs [1] of Yale, in response to a letter in Nature by the American physicist A. Michelson [2], presented a result about Fourier series that now goes by the name of the Gibbs…

The Gibbs' phenomenon

- Mathematics
- 2001

The well-known physicist A. A. Michelson started quite an interesting correspondence in the journal Nature in 1898. He complained about the convergence of continuous Fourier series approximations to…

A Simple Explanation of the Stokes Phenomenon

- Computer ScienceSIAM Rev.
- 1989

The Stokes Phenomenon is presented as a natural aspect of a well-motivated characterization of functions by approximands of different multivaluedness.

Differentiation of Fourier Series via Orthogonal Derivative

- Mathematics
- 2015

It is very known that if the operator d/dx acts on each term into a convergent Fourier Series (FS), then it may result a divergent series. This situation is remedied applying the symmetric derivative…

The Gibbs-Wilbraham phenomenon: An episode in fourier analysis

- Education
- 1979

plays an essential r61e in computing the amount of this overshoot. While teaching a course in the theory of functions of a real variable, E. HEWITT found the value 1.71... listed for the integral (1)…

On Gibbs constant for the Shannon wavelet expansion

- Computer Science
- 1997

By providing a sufficient condition to compute the size of Gibbs phenomenon for the Shannon wavelet series, the overshoot is propotional to the jump at discontinuity and by comparing it with that of the Fourier series, it is seen that these two have exactly the same Gibbs constant.

On gibb's phenomenon for sampling series in wavelet subspaces

- Mathematics
- 1996

Let {Vm be a multiresolution analysis of L2(R) such that a sampling function S for V0 exists. Then we show the sampling approximation of a function in H0,α1/2 onto Vm converges to it uniformly as…

Gibbs' phenomenon for sampling series and what to do about it

- Mathematics
- 1998

Gibbs' phenomenon occurs for most orthogonal wavelet expansions. It is also shown to occur with many wavelet interpolating series, and a characterization is given. By introducing modifications in…