Applications of Generating Functions

Description

Generating functions express a sequence as coefficients arising from a power series in variables. They have many applications in combinatorics and probability. In this paper, we will investigate the important properties of four kinds of generating functions in one variables: ordinary generating unction, exponential generating function, probability generating function and moment generating function. Many examples with applications in combinatorics and probability, will be discussed. Finally, some
well-known contest problems related to generating functions will be addressed.

Links & Downloads

1. http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0626107-134734

Tags

moment generating function

ordinary generating function

exponential generating function

probability generating function

recurrence relation

recurrence

binomial coefficient

binomial theorem

weak law of large numbers

central limit theorem

moment

probability distribution

variance

power series

identities

induction

counting problem

partition

Fibonacci

partial fractions

sequence

expectation

convolution

Additional Fields

Identifer	oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0626107-134734
Date	26 June 2007
Creators	Tseng, Chieh-Mei
Contributors	Mong-Na Lo Huang, Fu-Chuen Chang, Mei-Hui Guo
Publisher	NSYSU
Source Sets	NSYSU Electronic Thesis and Dissertation Archive
Language	Cholon
Detected Language	English
Type	text
Format	application/pdf
Source	http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0626107-134734
Rights	not_available, Copyright information available at source archive