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Abel Summability of Certain Series of Legendre Functions
Author(s) -
Love E. R.
Publication year - 1994
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/s3-69.3.629
Subject(s) - mathematics , legendre polynomials , legendre function , discontinuity (linguistics) , series (stratigraphy) , function series , convergence (economics) , simple (philosophy) , mathematical analysis , taylor series , function (biology) , pure mathematics , power series , paleontology , philosophy , epistemology , evolutionary biology , economics , biology , economic growth
A recent joint paper with M. N. Hunter contains convergence theory for some expansions of functions in bilateral series of Legendre functions. This paper contains convergence results for such series when the function expanded has a simple discontinuity at the point of expansion, a situation not previously covered. The method used is almost entirely different from that of the earlier paper; it proceeds via Abel summability and Littlewood's Tauberian Theorem.