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Excerpt from The Mathematician, Vol. 1
The coefficients now under consideration, are always introduced into analysis, subjected to a series of specified conditions and, as they never appear unaccompanied by these conditions, the term here chosen appears to be a very appropriate one. It is, therefore, adopted in the present and some succeeding papers in this work. This term has also the advantage of distinct and expressive application to another class of functions, nearly allied in its philosophical principles to this - known by the name of inde terminate multipliers. Or arbitrary multipliers. These multipliers are only introduced conditionally; that is, the several products are subjected to predetermined combinations, or made to fulfil certain specified conditions. It is, therefore, proposed to call these conditional multipliers.
The ordinary method of establishing the fundamental proposition respecting conditional coefficients, has often been objected to; and with good reason too, whether the following views shall be found correct, or not. It is, in fact, one of the most striking instances of what Berkeley terms shifting the hypothesis; that is, making a new hypothesis for the purposes of reasoning, which is inconsistent with the existence of the original one, upon which the proposition is founded. The method of making a: alternately zero and arbitrary is, however, the only one used in almost every work, even the most modern, that has been written for academical purposes, either in England or France. About eight years ago, however.
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The Mathematician, Vol. 1 (Classic Reprint)
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Paperback. Condizione: New. Print on Demand. This book analyzes and develops various elementary algebraic expansions. It begins by discussing conditional coefficients, which, this book explains, can be used as a tool for expanding functions in a series of terms with coefficients that are subject to specific conditions. The author then considers expansions by means of indeterminate multipliers or arbitrary multipliers. He highlights that these methods are more powerful than other expansion methods and can be used to expand functions in a variety of forms. The book concludes by exploring the application of these methods to specific problems, such as expanding binomial, multinomial, exponential, logarithmic, and trigonometric functions. By providing novel insights into the principles of expansion, this book is a valuable resource for students, researchers, and practitioners seeking to deepen their understanding of this fundamental mathematical concept and its diverse applications. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9780282254292_0
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The Mathematician, Vol. 1 (Classic Reprint)
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9780282254292
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The Mathematician, Vol. 1 (Classic Reprint)
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LW-9780282254292
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