The Stirling Numbers and Polynomials

Charles Tweedie

doi:10.1017/S0013091500035367

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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.

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* 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.

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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The Stirling Numbers and Polynomials

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