Title page for etd-0626107-134734


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URN etd-0626107-134734
Author Chieh-Mei Tseng
Author's Email Address No Public.
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Department Applied Mathematics
Year 2006
Semester 2
Degree Master
Type of Document
Language zh-TW.Big5 Chinese
Title Applications of Generating Functions
Date of Defense 2007-05-30
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
    well-known contest problems related to generating functions will be addressed.
    Advisory Committee
  • Mei-Hui Guo - chair
  • Mong-Na Lo Huang - co-chair
  • Fu-Chuen Chang - advisor
  • Files
  • etd-0626107-134734.pdf
  • indicate not accessible
    Date of Submission 2007-06-26

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