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Factorials and stirling numbers in the algebra of formal Laurent series

✍ Scribed by Heinrich Niederhausen

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
499 KB
Volume
90
Category
Article
ISSN
0012-365X

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✦ Synopsis

Niederhausen, H., Factorials and Stirling numbers in the algebra of formal Laurent series, Discrete Mathematics 90 (1991) 53-62.

In the algebra of formal Laurent series, the falling factoral powers x(") are generalized to {x}'") for all integers n. The Stirling coefficients map the standard basis of powers into the factorial powers. They comprise the Stirling numbers of both kinds, and a wedge of 'new' numbers, closely related to Bernoulli numbers of general order. {x}'"' can be used to construct a binomial series {i}, allowing for Vandermonde convolution and even a completely formal interpretation of (1 + t)@) as a Laurent series in t with coefficients being Laurent series in x.

which we call the algebra of lower Laurent series. Of course, we have to say how we are going to extend the two bases. The extension of x" is obvious. The falling

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