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Even those who are not specially interested in advanced thematics may find an elementary treatment of the subject of some value in giving them some knowledge of the subject at a first reading.\"","abstract_html":"Text from page 1-2: "It is the chief purpose of this paper to give a relatively simple proof for the possibility of representing a large class of functions by meansof convergent sine or cosine series, - generally classed as Fourier's Series. This seems desirable because of the growing importance of trigonometric series in their application to applied mathematics,along with their historical value in the development of the theory of functions and mathematicalanalysis. 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