We present numerical tests of several simple examples of center series,
with the aim of evaluating the speed with which they converge, as
compared to the corresponding Fourier series. These center series were
defined and developed in previous papers, and constitute an improved
form of trigonometric expansion of real functions, related to the
Fourier series. The tests performed are comparative ones, between each
Fourier series and the corresponding first-order center series. They
show that, specially in the case of Fourier series that converge very
slowly, the use of the center series can represent a truly enormous
numerical and computational advantage. We also use the numerical
advantage provided by the center series to display the Fourier Conjugate
functions of each example worked out, as well as to test the speed of
convergence of their Fourier series and first-order center series. For
the execution of the comparative tests between the Fourier and
first-order center series it was necessary, in some cases, to use also
the second-order center series, as tools for the tests, since these
converge even faster than the first-order center series.

- Introduction
- Tests of Center Series
- The One-Cycle Sawtooth Wave
- The Standard Square Wave
- The Two-Cycle Sawtooth Wave
- The Triangular Wave
- The Shifted Square Wave
- The Parabolic Wave
- The First Slow-Converging Case
- The Second Slow-Converging Case

- Summary of the Numerical Results
- Conclusions
- Acknowledgements
- Derivations of Center Series
- The One-Cycle Sawtooth Wave
- The Standard Square Wave
- The Two-Cycle Sawtooth Wave
- The Triangular Wave
- The Shifted Square Wave
- The Parabolic Wave
- The First Slow-Converging Case
- The Second Slow-Converging Case

- Numerical Results
- The One-Cycle Sawtooth Wave
- The Conjugate Function of the One-Cycle Sawtooth Wave
- The Standard Square Wave
- The Conjugate Function of the Standard Square Wave
- The Two-Cycle Sawtooth Wave
- The Conjugate Function of the Two-Cycle Sawtooth Wave
- The Triangular Wave
- The Conjugate Function of the Triangular Wave
- The Shifted Square Wave
- The Conjugate Function of the Shifted Square Wave
- The Parabolic Wave
- The Conjugate Function of the Parabolic Wave
- The First Slow-Converging Wave
- The Conjugate Function of the First Slow-Converging Wave
- The Second Slow-Converging Wave
- The Conjugate Function of the Second Slow-Converging Wave

- Bibliography