The general orthogonal series is represented by the equations:
This general formulation includes as special cases all of the commonly studied trigonometric fourier series. It includes as well, infinite series that involve Legendre Polynomials, Bessel functions, and other "Peoples Polynomials" such as Lagurre, Hermite, and Tchybecheff's polynomials.
This site gives links to files that may be used in conjunction with Mathematica to compute partial sums of all of these series and to study convergence properties for them. You may click on one of the following links to simply view plots of various partial sum approximations of some example functions.
Fourier Sine Series. |
Fourier Cosine Series. |
Fourier Full Range Series. |
More General Orthogonal Series. |
Bessel Functions J0(x). |
The following links will download Mathematica NoteBooks to study in depth some of the common special cases of orthogonal series.
| Fourier Sine Series. |
| Fourier Cosine Series. |
| Fourier Full Range Series. |
| Series using Legendre Polynomials. |
| Series using Bessel Functions
We have provided an assortment of problem/help files for these notebooks that may be printed in ordianry mathematical text format. They are avialable in various formats.