# OrthogonalPolys

* © 2017,2018 John Abbott, Anna M. Bigatti*

GNU Free Documentation License, Version 1.2

CoCoALib Documentation Index
## Examples

## User documentation

Here are some functions for constructing individual members of
certain families of orthogonal polynomials.

### Constructors and pseudo-constructors

Let `n`

be a non-negative integer, and `x`

a ring element
(typically an indeterminate or a number). The functions below
evaluate the corresponding polynomial at `x`

: if `x`

is an
indeterminate then the polynomial itself is returned.

`ChebyshevPoly(n,x)`

Chebyshev polynomial of 1st kind
`ChebyshevPoly2(n,x)`

Chebyshev polynomial of 2nd kind
`HermitePoly(n,x)`

Hermite polynomial (physics)
`HermitePoly2(n,x)`

Hermite polynomial (probability)
`LaguerrePoly(n,x)`

Laguerre polynomomial **multiplied** by `factorial(n)`

`DicksonPoly(x,n,alpha)`

Dickson polynomial of 1st type not orthog
`DicksonPoly2(x,n,alpha)`

Dickson polynomial of 2nd type not orthog

## Maintainer documentation

Some of the Chebyshev functions are not used, but I left them there
in case they ever become useful.

## Bugs, shortcomings and other ideas

The dispatch functions for Hermite polynomials have not been tested;
so I do not know if the criterion for choosing between "explicit" and
"iterative" implementations actually makes any sense.

## Main changes

**2017**

- October (v0.99560): first release
**2018**
- November (v0.99610): added DicksonPoly