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The theory uf the algebraic functions developed in the following pages is algebraic in its methods and perfectly general. It holds for any algebraic equation reducible or irreducible, however complicated its singularities may be and whatever its character at infinity. The development of the theory may be said to culminate in the comple mentary theorem, in Chapter XII, from which theorem a number of well-known theorems in the theory of the algebraic functions immediately follow as corollaries.
The principles here presented have been in the possession of the writer for some eight years past and had in fact, in a somewhat different form, already been written up with a view to publication in the summer of 1898. Other matters however inter vened and the work was laid aside for a long period. Since then further interruptions have occurred, the theory however has been twice rewritten in the interval and has probably lost nothing by the delay in publication. The writer has not felt it to be necessary to go into the theory of the Abelian integrals, his object having been attained on presenting the purely algebraic side of his subject.
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Paperback. Zustand: New. Print on Demand. This book offers a groundbreaking exploration of algebraic functions, providing a comprehensive theory that holds for any algebraic equation, no matter how complicated its singularities or character at infinity. The author, an esteemed mathematician, has spent years developing and refining this theory, which culminates in a groundbreaking theorem with far-reaching applications across the field of algebraic functions. The principles presented in this volume lay the foundation for further advancements in the theory of algebraic numbers and functions of multiple variables. Through a novel representation of algebraic function branches near singular manifolds, the author opens up new avenues for research and problem-solving. This book is an invaluable resource for mathematicians seeking to deepen their understanding of algebraic functions and their 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. Bestandsnummer des Verkäufers 9781330185988_0
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