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Titlebook: Generating Functions in Engineering and the Applied Sciences; Rajan Chattamvelli,Ramalingam Shanmugam Book 2023Latest edition The Editor(s

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书目名称Generating Functions in Engineering and the Applied Sciences
编辑Rajan Chattamvelli,Ramalingam Shanmugam
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概述Provides broad exposure to commonly used techniques of combinatorial mathematics.Introduces commonly encountered generating functions for researchers working in economics, finance, and statistics.Deve
丛书名称Synthesis Lectures on Engineering, Science, and Technology
图书封面Titlebook: Generating Functions in Engineering and the Applied Sciences; Rajan Chattamvelli,Ramalingam Shanmugam Book 2023Latest edition The Editor(s
描述.Generating function (GF) is a mathematical technique to concisely represent a known ordered sequence into a simple continuous algebraic function in dummy variable(s). This Second Edition introduces commonly encountered generating functions (GFs) in engineering and applied sciences, such as ordinary GF (OGF), exponential GF (EGF), as also Dirichlet GF (DGF), Lambert GF (LGF), Logarithmic GF (LogGF), Hurwitz GF (HGF), Mittag-Lefler GF (MLGF), etc.  This book is intended mainly for beginners in applied science and engineering fields to help them understand single-variable GFs and illustrate how to apply them in various practical problems.  Specifically, the book discusses probability GFs (PGF),  moment and cumulant GFs (MGF, CGF), mean deviation GFs (MDGF), survival function GFs (SFGF), rising and falling factorial GFs, factorial moment, and inverse factorial moment GFs.  Applications of GFs in algebra, analysis of algorithms, bioinformatics, combinatorics, economics, finance, genomics, geometry, graph theory, management, number theory, polymer chemistry, reliability, statistics and structural engineering have been added to this new edition. This book is written in such a way that re
出版日期Book 2023Latest edition
关键词Generating Function Applications; Generating Functions in Statistics; Operations on Generating Functio
版次2
doihttps://doi.org/10.1007/978-3-031-21143-0
isbn_softcover978-3-031-21145-4
isbn_ebook978-3-031-21143-0Series ISSN 2690-0300 Series E-ISSN 2690-0327
issn_series 2690-0300
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
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Remarks on the Nakano Vanishing Theorem,Generating function is a mathematical technique to concisely represent a known ordered sequence into a simple algebraic function. In essence, it takes a sequence as input, and produces a continuous function in one or more dummy (arbitrary) variables as output. A sequence is an ordered succession of elements which may be finite or infinite.
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https://doi.org/10.1007/978-3-642-46893-3The first chapter explored several simple sequences. As a sequence is indexed by natural numbers, the best way to express an arbitrary term of a sequence seems to be a closed form as a function of the index (.).
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The Quasi-Optimizer (QO) System,GFs are used in various branches of statistics like distribution theory, stochastic processes, etc. A one-to-one correspondence is established between the power series expansion of a GF in one or more auxiliary (dummy) variables, and the coefficients of a known sequence.
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https://doi.org/10.1007/978-94-010-2182-1There are many applications of GFs in algebra. GFs can be used to find the number of solutions to a single linear equation. Consider a simple example of an equation ., where ., ., . are non-negative integers, and . is a constant. Consider the OGF ..
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Types of Generating Functions,Generating function is a mathematical technique to concisely represent a known ordered sequence into a simple algebraic function. In essence, it takes a sequence as input, and produces a continuous function in one or more dummy (arbitrary) variables as output. A sequence is an ordered succession of elements which may be finite or infinite.
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Operations on Generating Functions,The first chapter explored several simple sequences. As a sequence is indexed by natural numbers, the best way to express an arbitrary term of a sequence seems to be a closed form as a function of the index (.).
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