## org.jscience.mathematics.analysis.polynomials Interface OrthogonalPolynomialFactory

All Known Implementing Classes:
ChebyshevDoublePolynomialFactory, GegenbauerDoublePolynomialFactory, HermiteDoublePolynomialFactory, JacobiDoublePolynomialFactory, LaguerreDoublePolynomialFactory, LegendreDoublePolynomialFactory, OrthogonalDoublePolynomialFactory, OrthogonalExactRealPolynomialFactory, SecondKindChebyshevDoublePolynomialFactory

`public interface OrthogonalPolynomialFactory`

This class is the base class for orthogonal polynomials.

Orthogonal polynomials can be defined by recurrence relations like:

```      O0(X)   = some 0 degree polynomial
O1(X)   = some first degree polynomial
a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X)
```
where a0k, a1k, a2k and a3k are simple expressions which either are constants or depend on k.

Method Summary
` Polynomial[]` `getFirstTermsPolynomials()`
Initialize the recurrence coefficients for degree 0 and 1.
` Polynomial` `getOrthogonalPolynomial(int degree)`
DOCUMENT ME!
` Field.Member[]` `getRecurrenceCoefficients(int k)`
Initialize the recurrence coefficients.

Method Detail

### getOrthogonalPolynomial

`Polynomial getOrthogonalPolynomial(int degree)`
DOCUMENT ME!

Parameters:
`degree` - DOCUMENT ME!
Returns:
DOCUMENT ME!

### getFirstTermsPolynomials

`Polynomial[] getFirstTermsPolynomials()`
Initialize the recurrence coefficients for degree 0 and 1.

Returns:
an array which contains the coefficients for degree 0 and 1

### getRecurrenceCoefficients

`Field.Member[] getRecurrenceCoefficients(int k)`
Initialize the recurrence coefficients. The recurrence relation is
`a1k Ok+1(X) = (a2k + a3k X) Ok(X) - a4k Ok-1(X)`

Parameters:
`k` - index of the current step
Returns:
a double array of 3 elements: b2k = double[0] coefficient to initialize (b2k = a2k / a1k) b3k = double[1] coefficient to initialize (b3k = a3k / a1k) b4k = double[2] coefficient to initialize (b4k = a4k / a1k)