✦ LIBER ✦

Fast Lagrange inversion, with an application to factorial numbers

✍ Scribed by Heinrich Niederhausen

Publisher: Elsevier Science
Year: 1992
Tongue: English
Weight: 630 KB
Volume: 104
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)90628-s

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✦ Synopsis

Niederhausen, H., Fast Lagrange inversion, with an application to factorial numbers, Discrete Mathematics 104 (1992) 99-110. Suppose /3(t) and y(t) are a pair of compositional inverse formal powerseries. Lagrange inversion expresses the coefficient oft" in y(t)" in terms of the coefficient of tC" in /c?(t)-". 'Fast Lagrange inversion' calculate the latter for invertible power series with nonzero quadratic term, using only positive powers of /?. The result is given for multivariate series, and illustrated by a bivariate generalization of Stirling numbers.

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