000 06548nam a2200913 i 4500
001 8826061
003 IEEE
005 20200413152933.0
006 m eo d
007 cr cn |||m|||a
008 190927s2019 cau fob 001 0 eng d
020 _a9781681736396
_qelectronic
020 _z9781681736402
_qhardcover
020 _z9781681736389
_qpaperback
024 7 _a10.2200/S00942ED1V01Y201907ENG037
_2doi
035 _a(CaBNVSL)thg00979524
035 _a(OCoLC)1119624973
040 _aCaBNVSL
_beng
_erda
_cCaBNVSL
_dCaBNVSL
050 4 _aQA353.G44
_bC534 2019eb
082 0 4 _a515/.55
_223
100 1 _aChattamvelli, Rajan,
_eauthor.
245 1 0 _aGenerating functions in engineering and the applied sciences /
_cRajan Chattamvelli, Ramalingam Shanmugam.
264 1 _a[San Rafael, California] :
_bMorgan & Claypool,
_c[2019]
300 _a1 PDF (xiii, 97 pages).
336 _atext
_2rdacontent
337 _aelectronic
_2isbdmedia
338 _aonline resource
_2rdacarrier
490 1 _aSynthesis lectures on engineering,
_x1939-523X ;
_v#37
538 _aMode of access: World Wide Web.
538 _aSystem requirements: Adobe Acrobat Reader.
500 _aPart of: Synthesis digital library of engineering and computer science.
504 _aIncludes bibliographical references (page 91) and index.
505 0 _a1. Types of generating functions -- 1.1. Introduction -- 1.2. Notations and nomenclatures -- 1.3. Types of generating functions -- 1.4. Ordinary generating functions -- 1.5. Exponential generating functions (EGF) -- 1.6. Pochhammer generating functions -- 1.7. Other generating functions -- 1.8. Summary
505 8 _a2. Operations on generating functions -- 2.1. Basic operations -- 2.2. Invertible sequences -- 2.3. Composition of generating functions -- 2.4. Summary
505 8 _a3. Generating functions in statistics -- 3.1. Generating functions in statistics -- 3.2. Probability generating functions (PGF) -- 3.3. Generating functions for CDF -- 3.4. Generating functions for survival functions -- 3.5. Generating functions for mean deviation -- 3.6. MD of some distributions -- 3.7. Moment generating functions (MGF) -- 3.8. Characteristic functions -- 3.9. Cumulant generating functions -- 3.10. Factorial moment generating functions -- 3.11. Conditional moment generating functions (CMGF) -- 3.12. Generating functions of truncated distributions -- 3.13. Convergence of generating functions -- 3.14. Summary
505 8 _a4. Applications of generating functions -- 4.1. Applications in algebra -- 4.2. Applications in computing -- 4.3. Applications in combinatorics -- 4.4. Applications in graph theory -- 4.5. Applications in chemistry -- 4.6. Applications in epidemiology -- 4.7. Applications in number theory -- 4.8. Applications in statistics -- 4.9. Generating functions in reliability -- 4.10. Applications in bioinformatics -- 4.11. Applications in genetics -- 4.12. Applications in management -- 4.13. Applications in economics -- 4.14. Summary.
506 _aAbstract freely available; full-text restricted to subscribers or individual document purchasers.
510 0 _aCompendex
510 0 _aINSPEC
510 0 _aGoogle scholar
510 0 _aGoogle book search
520 _aThis is an introductory book on generating functions (GFs) and their applications. It discusses commonly encountered generating functions in engineering and applied sciences, such as ordinary generating functions (OGF), exponential generating functions (EGF), probability generating functions (PGF), etc. Some new GFs like Pochhammer generating functions for both rising and falling factorials are introduced in Chapter 2. Two novel GFs called "mean deviation generating function" (MDGF) and "survival function generating function" (SFGF), are introduced in Chapter 3. The mean deviation of a variety of discrete distributions are derived using the MDGF. The last chapter discusses a large number of applications in various disciplines including algebra, analysis of algorithms, polymer chemistry, combinatorics, graph theory, number theory, reliability, epidemiology, bio-informatics, genetics, management, economics, and statistics. Some background knowledge on GFs is often assumed for courses in analysis of algorithms, advanced data structures, digital signal processing (DSP), graph theory, etc. These are usually provided by either a course on "discrete mathematics" or "introduction to combinatorics." But, GFs are also used in automata theory, bio-informatics, differential equations, DSP, number theory, physical chemistry, reliability engineering, stochastic processes, and so on. Students of these courses may not have exposure to discrete mathematics or combinatorics. This book is written in such a way that even those who do not have prior knowledge can easily follow through the chapters, and apply the lessons learned in their respective disciplines. The purpose is to give a broad exposure to commonly used techniques of combinatorial mathematics, highlighting applications in a variety of disciplines.
530 _aAlso available in print.
588 _aTitle from PDF title page (viewed on September 27, 2019).
650 0 _aGenerating functions.
653 _aalgebra
653 _aanalysis of algorithms
653 _abio-informatics
653 _aCDF generating functions
653 _acombinatorics
653 _acumulants
653 _adifference equations
653 _adiscrete mathematics
653 _aeconomics
653 _aepidemiology
653 _afinance
653 _agenetics
653 _agraph theory
653 _amanagement
653 _amean deviation generating function
653 _amoments
653 _anumber theory
653 _aPochhammer generating functions
653 _apolymer chemistry
653 _apower series
653 _arecurrence relations
653 _areliability engineering
653 _aspecial numbers
653 _astatistics
653 _astrided sequences
653 _asurvival function
653 _atruncated distributions.
700 1 _aShanmugam, Ramalingam,
_eauthor.
776 0 8 _iPrint version:
830 0 _aSynthesis digital library of engineering and computer science.
830 0 _aSynthesis lectures on engineering ;
_v#37.
856 4 2 _3Abstract with links to resource
_uhttps://ieeexplore.ieee.org/servlet/opac?bknumber=8826061
856 4 0 _3Abstract with links to full text
_uhttps://doi.org/10.2200/S00942ED1V01Y201907ENG037
999 _c562431
_d562431