Fourier series Articles

Tag Archive for: Fourier series

Fourier Series Riemann Zeta Function

Computing the Riemann Zeta Function Using Fourier Series

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Euler's amazing identity The mathematician Leonard Euler developed some surprising mathematical formulas involving the number ##\pi##. The most famous…
Odd Sums

Explore the Fascinating Sums of Odd Powers of 1/n

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The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…
fourierseries2

Learn Further Sums Found Through Fourier Series

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In an earlier insight, I looked at the Fourier series for some simple polynomials and what we could deduce from those series. There is a lot more to be…
FourierSeries

Using the Fourier Series To Find Some Interesting Sums

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Preliminaries If f(x) is periodic with period 2p and f’(x) exists and is finite for -π<x<π, then f can be written as a Fourier series: [itex]f(x)=\sum_{n=-\infty}^{\infty}a_{n}e^{inx}…
differentiable function 2

Nowhere Differentiable Functions: Fejér Kernel & Cesàro Sums

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This is Part 2 of a series of articles in which the goal is to exhibit a continuous function that is nowhere differentiable and to explore some interesting…
differentiable function

Constructing a Continuous but Nowhere Differentiable Function

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When studying calculus, we learn that every differentiable function is continuous, but a continuous function need not be differentiable at every point.…