arXiv subjects

German A. Kalugin

Publications and source records attributed to German A. Kalugin.

2 recordsLinked to original sources

arXiv2012

Convergence in $\C$ of series for the Lambert $W$ Function

We study some series expansions for the Lambert $W$ function. We show that known asymptotic series converge in both real and complex domains. We establish the precise domains of convergence and other properties of the series, including asymptotic expressions for the expansion coefficients. We introduce an new invariant transformation of the series. The transformation contains a parameter whose effect on the domain and rate of convergence is studied theoretically and numerically. We also give alternate representations of the expansion coefficients, which imply a number of combinatorial identities.

math.CA↗

arXiv2011

Stieltjes, Poisson and other integral representations for functions of Lambert $W$

We show that many functions containing $W$ are Stieltjes functions. Explicit Stieltjes integrals are given for functions $1/W(z)$, $W(z)/z$, and others. We also prove a generalization of a conjecture of Jackson, Procacci & Sokal. Integral representations of $W$ and related functions are also given which are associated with the properties of their being Pick or Bernstein functions. Representations based on Poisson and Burniston--Siewert integrals are given as well.

math.CV↗