On the inversion of $y^αe^y$ in terms of associated Stirling numbers

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dc.creatorJeffrey, David J.
dc.creatorCorless, Robert M.
dc.creatorHare, David E. G.
dc.creatorKnuth, Donald E.
dc.date1995-12-01
dc.date.accessioned2026-07-07T09:15:26Z
dc.date.available2026-07-07T09:15:26Z
dc.descriptionThe function $y=Φ_α(x)$, the solution of $y^αe^y=x$ for $x$ and $y$ large enough, has a series expansion in terms of $\ln x$ and $\ln\ln x$, with coefficients given in terms of Stirling cycle numbers. It is shown that this expansion converges for $x>(αe)^α$ for $α\ge 1$. It is also shown that new expansions can be obtained for $Φ_α$ in terms of associated Stirling numbers. The new expansions converge more rapidly and on a larger domain.
dc.identifierhttps://arxiv.org/abs/math/9512230
dc.identifierhttp://arxiv.org/abs/math/9512230
dc.identifierC. R. Acad. Sci. Paris Sér. I Math. 320 (1995), no. 12, 1449--1452
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/153018
dc.subjectClassical Analysis and ODEs
dc.titleOn the inversion of $y^αe^y$ in terms of associated Stirling numbers
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