Orthogonal Polynomials | Extreme Optimization Numerical Libraries for .NET Professional |

Orthogonal polynomials arise in phsysics, engineering and other areas as the solutions to certain differential equations.

The **Extreme Optimization Numerical Libraries for .NET**
provide support for the most common types: Chebyshev polynomials of the first and
second kind, Hermite polynomials, Legendre polynomials, Laguerre and
generalized Laguerre polynomials, and Gegenbauer polynomials.

Methods are provided for the evaluation of a single polynomial of the specified degree at a point, of a sequence of polynomials of increasing degree, and of a series or a linear combination of polynomials of increasing degree.

The names of these methods follow a consistent pattern. The base name is made up of the name of the polynomial followed by the conventional mathematical abbreviation. For example, the base name for Chebyshev polynomials of the first kind is ChebyshevT. The following table lists the base names for the supported polynomials:

Base name | Description |
---|---|

ChebyshevT | Chebyshev polynomials of the first kind, T |

ChebyshevU | Chebyshev polynomials of the second kind, U |

HermiteH | Hermite polynomials, H |

LaguerreL | Laguerre polynomials, L |

GegenbauerC | Gegenbauer polynomials,
C |

LegendreP | Legendre polynomials, P |

The base method evaluates the polynomial of a specified degree at a point.
With Sequence appended to the base name, the
method evaluates a sequence of polynomials of increasing order.
Optional parameters let you specify the degree of the first polynomial
in the sequence and a
Vector

Method | Description |
---|---|

Evaluates the Chebyshev polynomial of the first kind. | |

Evaluates the Chebyshev polynomial of the first kind. | |

Evaluates a linear combination of Chebyshev polynomial of the first kind. |

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