Definition:Generating Function/Historical Note
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Historical Note on Generating Function
Generating functions were introduced by Abraham de Moivre to solve the general problem of linear recurrences.
James Stirling then extended this theory in his Methodus Differentialis of $1730$, by using differentiation and integration.
Then Leonhard Paul Euler began extending their use to new fields such as combinatorics.
Pierre-Simon de Laplace took the technique into the field of probability theory in his $1812$ work Théorie Analytique des Probabilités
Many others since have developed the technique further.
- A generating function is a clothesline on which we hang up a sequence of numbers for display.
- -- 1990: Herbert S. Wilf: generatingfunctionology
- 1741: Leonhard Paul Euler: Observationes Analyticae Variae de Combinationibus (Commentarii Acad. Sci. Imp. Pet. Vol. 13: pp. 64 – 93)
- 1750: Leonhard Paul Euler: De Partitione Numerorum (Novi Comment. Acad. Sci. Imp. Petropol. Vol. 3: pp. 125 – 169)
- 1923: E.T. Bell: Euler Algebra (Trans. Amer. Math. Soc. Vol. 25: pp. 135 – 154) www.jstor.org/stable/1989055
- 1969: Ivan Niven: Formal Power Series (Amer. Math. Monthly Vol. 76: pp. 871 – 889) www.jstor.org/stable/2317940
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.9$: Generating Functions