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Titlebook: Quantum Calculus; Victor Kac,Pokman Cheung Textbook 2002 Victor Kac. 2002 Derivative.Hypergeometric function.Partition.Quantum Calculus.Qu

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书目名称Quantum Calculus
编辑Victor Kac,Pokman Cheung
视频video
概述Includes supplementary material:
丛书名称Universitext
图书封面Titlebook: Quantum Calculus;  Victor Kac,Pokman Cheung Textbook 2002 Victor Kac. 2002 Derivative.Hypergeometric function.Partition.Quantum Calculus.Qu
描述In one sentence, quantum calculus is the ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, we discover, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by the second author over the last few years at MIT.
出版日期Textbook 2002
关键词Derivative; Hypergeometric function; Partition; Quantum Calculus; Quantum Groups; calculus; combinatorics
版次1
doihttps://doi.org/10.1007/978-1-4613-0071-7
isbn_softcover978-0-387-95341-0
isbn_ebook978-1-4613-0071-7Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightVictor Kac. 2002
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发表于 2025-3-21 22:58:00 | 显示全部楼层
Properties of ,-Binomial Coefficients,cover the ordinary binomial coefficients if we take . → 1, we expect their .-analogues to have similar properties. Firstly, as already remarked in (5.4), . follows exactly the classical result. However, the correspondence is more subtle for another identity of binomial coefficients, the Pascal rule:
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0172-5939 evelops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, we discover, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a f
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,-Taylor’s Formula for Formal Power Series and Heine’s Binomial Formula,e. It is “formal” because often we do not worry about whether the series converges or not, and we can operate on (for example, differentiate) the series formally. We have to assume . and . to be zero in order to avoid divergence problems. Of course, .(0) = . by definition.
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