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The Stirling Numbers and Polynomials

Published online by Cambridge University Press:  20 January 2009

Charles Tweedie
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Extract

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If we write the product

in the form

the coefficients have been called by Professor Nielsen (following Thiele) the Stirling Numbers of the First Species, because James Stirling, in his Methodus Differentialis (1730), was the first writer to draw attention to their use, and furnished a small table of their initial values.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 37 , February 1918 , pp. 2 - 25
Copyright
Copyright © Edinburgh Mathematical Society 1918

References

* Page 11 and page 8, Meth. Diff.

* These theorems are only true if r is independent of n. For example, since , all the numbers cannot be divisible by n (n – l ). A similar restriction applies to the presence of a square factor in the Bernoullian Polynomials of even degree.