Abstract
In this chapter we briefly discuss the powerful method of generating functions, i.e., the use of power series in the analysis of counting problems that are inaccessible by the more elementary techniques presented so far.
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Notes
- 1.
We shall sometimes refer to the generating function of a sequence (a n )n≥1 of real numbers, but this should be no source of confusion.
- 2.
As quoted in [8], Newton is considered to be one of the greatest scientists ever, being difficult to properly address the scope of his contributions to the development of science.
- 3.
- 4.
After Eugène Catalan , Belgian mathematician of the nineteenth century.
References
T. Apostol, Calculus, Vol. 1 (Wiley, New York, 1967)
A. Caminha, An Excursion Through Elementary Mathematics I - Real Numbers and Functions (Springer, New York, 2017)
R. Honsberger, Mathematical Gems III (Washington, MAA, 1985)
W. Rudin, Principles of Mathematical Analysis, 3rd edn. (McGraw-Hill, Inc., New York, 1976)
H. Wilf, Generatingfunctionology (Academic, San Diego, 1990)
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Caminha Muniz Neto, A. (2018). Generating Functions. In: An Excursion through Elementary Mathematics, Volume III. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-77977-5_3
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DOI: https://doi.org/10.1007/978-3-319-77977-5_3
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