Chapter authors: Ranjan Roy, Frank W. J. Olver, Richard A. Askey, Roderick S. C. Wong, William P. Reinhardt. Their names are given on the official chapter landing page.
Online text: dlmf.nist.gov/1
Cited section: dlmf.nist.gov/1.10
Cited passages: §1.10(iv), equation 1.10.9, states the argument principle; equation 1.10.10 gives the multiplicity-weighted sum of zero locations minus pole locations used in the weighted argument principle.
Cited passage: §1.11(ii), equation 1.11.10, gives the coefficient relations used in elementary symmetric polynomial.
Online text: dlmf.nist.gov/5.2