Journal article
Jacobi series which converge to zero, with applications to a class of singular partial differential equations
Mathematical proceedings of the Cambridge Philosophical Society, v 65(1), pp 101-106
Jan 1969
Abstract
Expansions in series of functions are one of the most important tools of the applied mathematician, particularly expansions in series of the classical orthogonal polynomials, e.g. Laguerre, Jacobi and Hermite polynomials. In applied problems, the uniqueness of the particular expansion is usually intrinsic to the analysis, and often implicitly assumed. Indeed, in those cases where the functions in the series are orthogonal, uniqueness can often be proved by an argument that runs as follows. Let {φn(x)} (n = 0, 1, 2, …) be a sequence of functions orthogonal with respect to the weight function ρ(x) over the interval [0, 1], and suppose that the series being boundedly convergent for 0 ≤ x ≤ 1.
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Details
- Title
- Jacobi series which converge to zero, with applications to a class of singular partial differential equations
- Creators
- Jet Wimp - MRIGlobalDavid Colton - MRIGlobal
- Publication Details
- Mathematical proceedings of the Cambridge Philosophical Society, v 65(1), pp 101-106
- Publisher
- Cambridge University Press
- Number of pages
- 6
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Scopus ID
- 2-s2.0-84971184272
- Other Identifier
- 991021879788104721