[jira] [Updated] (MATH-687) Add the Jacobi polynomials in the class PolynomialsUtils

["DI COSTANZO (Updated) (JIRA)" <ji...@apache.org>]

     [ https://issues.apache.org/jira/browse/MATH-687?page=com.atlassian.jira.plugin.system.issuetabpanels:all-tabpanel ]

DI COSTANZO updated MATH-687:
-----------------------------

    Attachment: jacobi.patch

Here is the patch for the Jacobi polynomials. This implementation is using a Map of JacobiKey to store every computed polynomials for a given key value (u,v). The cache process is used and some test have been added in to the PolynomialsUtilsTest class.
                
> Add the Jacobi polynomials in the class PolynomialsUtils
> --------------------------------------------------------
>
>                 Key: MATH-687
>                 URL: https://issues.apache.org/jira/browse/MATH-687
>             Project: Commons Math
>          Issue Type: New Feature
>    Affects Versions: 3.0
>         Environment: all
>            Reporter: DI COSTANZO
>            Priority: Trivial
>         Attachments: jacobi.patch
>
>
> Jacobi polynomials Pk(vw) are a generalization of the legendre polynomial. Legendre Polynomials are Jacobi polynomials for v = w = 0.
> They are orthogonal polynomials and are defined from a recursion formula, giving the n+1 element of the polynomial from the nth element and the (n-1)'s one
> Therefore, they could be implemented in the PolynomialsUtils and use the generic frame already used in this class to create and store them.

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