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1	Applications of Generating Functions Tseng, Chieh-Mei 26 June 2007 (has links) 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. 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