Open AccessOn a mode of generating fourier series
Author(s) -
William Young
Publication year - 1911
Publication title -
proceedings of the royal society of london. series a, containing papers of a mathematical and physical character
Language(s) - English
Resource type - Journals
eISSN - 2053-9150
pISSN - 0950-1207
DOI - 10.1098/rspa.1911.0055
Subject(s) - series (stratigraphy) , fourier series , scope (computer science) , fourier transform , argument (complex analysis) , function (biology) , mode (computer interface) , mathematics , computer science , mathematical analysis , medicine , paleontology , evolutionary biology , biology , programming language , operating system
§ 1. In a recent paper published in the 'Proceedings' of this Society I obtained formulæ for the sum of the series formed by the Fourier constants: of a function, when each of these is divided by a power of the index giving its place in the series. As I there remarked, the scope of these results is really wider than at first appears, and I undertook to develop later their further consequences. The present communication is the outcome of this undertaking. I have, however, already in part indicated in a second still more recent paper the general nature of the argument which I propose to employ. I start with a Fourier seriesf (x ) ∼ Ʃ∞ n = 1(an cosnx +bn sinnx ), and its allied series Ʃ∞ n = 1(-an sinnx +bn cosnx ).