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On the Convergence of Fourier‐Bessel Series
Author(s) -
Young L. C.
Publication year - 1942
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s2-47.1.290
Subject(s) - convergence (economics) , bessel function , citation , series (stratigraphy) , mathematics , fourier series , mathematics education , library science , computer science , mathematical analysis , paleontology , economics , biology , economic growth
where, in the notation of Watson's book on Bessel functions!, * e expression w !r denotes the Bessel function of order v of the first kind, and j m is its m-th positive zero in ascending order of magnitude. The index v is fixed in (1.1) and we suppose, with Watson f, that (1.3) v+i^Q. It is convenient to stipulate further, unless the contrary is explicitly stated, that we have (1.4) x*f(x) = 0 when x = 0 and when x= 1, in view of the fact that the functions (1.1) vanish at the end points 0 and 1. The problem of the convergence of our series in the partial interval e 0, may be regarded as settled by the memoir of