The Lah Numbers and thenth Derivative of e1/x

DOI10.4169/math.mag.86.1.039zbMath1274.05014OpenAlexW2085328222MaRDI QIDQ2859038

Jan Mangaldan, Michael Z. Spivey, Siad Daboul, Peter J. Taylor

Publication date: 6 November 2013

Published in: Mathematics Magazine (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4169/math.mag.86.1.039

zbMATH Keywords

Poisson distributionLah numbersMaclaurin seriescoefficients in the \(n\)th derivative of \(e^{1/x}\)Fàa di Bruno's formulaKummer's hypergeometric transformation

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19)

Related Items (12)

Explicit expressions for a family of the Bell polynomials and applications ⋮ Unnamed Item ⋮ Unnamed Item ⋮ \(B_{n -1}\)-bundles on the flag variety. II ⋮ Explicit formulas and identities for the Bell polynomials and a sequence of polynomials applied to differential equations ⋮ Derivatives of tangent function and tangent numbers ⋮ An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers ⋮ Lah numbers, Laguerre polynomials of order negative one, and the \(n\)th derivative of \(\exp(1/x)\) ⋮ Applications of the formula of Faà di Bruno: combinatorial identities and monotonic functions ⋮ On complete monotonicity for several classes of functions related to ratios of gamma functions ⋮ Lah distribution: Stirling numbers, records on compositions, and convex hulls of high-dimensional random walks ⋮ A Nearly Forgotten Formula: Halphen’s Identity for Derivatives and Beyond

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