Orthogonality of Jacobi polynomials with general parameters.
In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to ei...
| Príomhchruthaitheoirí: | , , |
|---|---|
| Formáid: | info:eu-repo/semantics/article |
| Teanga: | English |
| Foilsithe / Cruthaithe: |
2012
|
| Ábhair: | |
| Rochtain ar líne: | http://hdl.handle.net/10835/1636 |
| Achoimre: | In this paper we study the orthogonality conditions satisfied by Jacobi polynomials $P_n^{(\alpha,\beta)}$ when the parameters $\alpha$ and $\beta$ are not necessarily $>-1$. We establish orthogonality on a generic closed contour on a Riemann surface. Depending on the parameters, this leads to either full orthogonality conditions on a single contour in the plane, or to multiple orthogonality conditions on a number of contours in the plane. In all cases we show that the orthogonality conditions characterize the Jacobi polynomial $P_n^{(\alpha, \beta)}$ of degree $n$ up to a constant factor. |
|---|