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Close Encounters with the Stirling Numbers of the Second Kind

Year of Award: 2013

Award: Allendoerfer

Publication Information: Mathematics Magazine, vol. 85, 2012, pp. 252-266 

Summary: The Scottish mathematician James Stirling, in his 1730 book Methodus Differentialis, explored Newton series, which are expansions of functions in terms of difference polynomials. The coefficients of these polynomials, computed using finite differences, are the Stirling numbers of the second kind. The article visits the work of Stirling, Newton, Grünert, Euler and Jacob Bernoulli. The author uses an analytical approach that mixes combinatorics and analysis.

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About the Author: (From the MathFest 2013 Prizes and Awards Booklet)

Khristo Boyadzhiev is a Professor of Mathematics at Ohio Northern University. He was born and educated in
Sofia, Bulgaria
. Khristo enrolled at Sofia University, "St. Kliment Ohridski", with the intention to study physics, but the
calculus lectures of Yaroslav Tagamlitski changed his mi
nd. Later Tagamlitski became his PhD advisor.

At the beginning of his career Khristo was interested mostly in Banach algebras and operator theory. Later in life
he developed a steady interest in classical analysis
.

He is married and has two daughters. In his spare time Khristo enjoys blogging, taking long walks around the
beautiful ONU campus
, and listening to classical music.

 

 

 

MSC Codes: 
11B73
Author(s): 
Khristo N. Boyadzhiev (Ohio Northern University)
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Publication Date: 
Saturday, August 17, 2013
Publish Page: 
Summary: 

Summary (adapted from the Prizes and Awards booklet for MathFest 2013)

The Scottish mathematician James Stirling, in his 1730 book Methodus Differentialis, explored Newton series, which are expansions of functions in terms of difference polynomials. The coefficients of these polynomials, computed using finite differences, are the Stirling numbers of the second kind. The article visits the work of Stirling, Newton, Grünert, Euler and Jacob Bernoulli. The author uses an analytical approach that mixes combinatorics and analysis.

 

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