Journal article
Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
Canadian journal of mathematics, v 39(4), pp 983-1000
01 Aug 1987
Abstract
In this paper we determine closed-form expressions for the associated Jacobi polynomials, i.e., the polynomials satisfying the recurrence relation for Jacobi polynomials with n replaced by n + c, for arbitrary real c ≧ 0. One expression allows us to give in closed form the [n — 1/n] Padé approximant for what is essentially Gauss' continued fraction, thus completing the theory of explicit representations of main diagonal and off-diagonal Padé approximants to the ratio of two Gaussian hypergeometric functions and their confluent forms, an effort begun in [2] and [19]. (We actually give only the [n — 1/n] Padé element, although other cases are easily constructed, see [19] for details.) We also determine the weight function for the polynomials in certain cases where there are no discrete point masses. Concerning a weight function for these polynomials, so many writers have obtained so many partial results that our formula should be considered an epitome rather than a real discovery, see the discussion in Section 3.
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Details
- Title
- Explicit Formulas for the Associated Jacobi Polynomials and Some Applications
- Creators
- Jet Wimp - Drexel University
- Publication Details
- Canadian journal of mathematics, v 39(4), pp 983-1000
- Publisher
- Cambridge University Press
- Number of pages
- 18
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1987L680700014
- Other Identifier
- 991019312462804721
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- Web of Science research areas
- Mathematics