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Discrete Calculus through generating functions (Wai Yan Pong, Cal State Dominguez Hills)
April 11, 2023 @ 12:15 pm - 1:10 pm
Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate a function with a sequence so that the coefficients of the power series expansion of the function represent the terms of the sequence. They provide a systematic way to encode information about a sequence or a combinatorial structure in a single function, which can then be manipulated algebraically to obtain various types of results. In this talk, we will examine a few well-known results about binomial coefficients, Stirling numbers and Bernoulli numbers using both Discrete Calculus and generating functions as well as the interaction between them.