# 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.

## 234 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

- Computer Science
- 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

- Mathematics, 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

- Philosophy
- 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

- Mathematics
- 1997

Even though the Shannon wavelet is a prototype of wavelets, it lacks condition on decay which most wavelets are assumed to have. By providing a sufficient condition to compute the size of Gibbs…

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…