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...
| প্রধান লেখক: | , , |
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| বিন্যাস: | info:eu-repo/semantics/article |
| ভাষা: | English |
| প্রকাশিত: |
2012
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | http://hdl.handle.net/10835/1636 |
| সংক্ষিপ্ত: | 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. |
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