URN 
etd0626107134734 
Author 
ChiehMei Tseng 
Author's Email Address 
No Public. 
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Department 
Applied Mathematics 
Year 
2006 
Semester 
2 
Degree 
Master 
Type of Document 

Language 
zhTW.Big5 Chinese 
Title 
Applications of Generating Functions 
Date of Defense 
20070530 
Page Count 
81 
Keyword 
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

Abstract 
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 wellknown contest problems related to generating functions will be addressed. 
Advisory Committee 
MeiHui Guo  chair
MongNa Lo Huang  cochair
FuChuen Chang  advisor

Files 
indicate not accessible 
Date of Submission 
20070626 