lgarchLogl returns the log-likelihood of the ARMA representation, whereas lgarchRecursion1 returns the residuals of the ARMA representation associated with parameters pars
Details
To understand the structure and content of pars and aux, see the source code of the lgarch function
References
Sucarrat, Gronneberg and Escribano (2013), 'Estimation and Inference in Univariate and Multivariate Log-GARCH-X Models When the Conditional Density is Unknown', MPRA Paper 49344: http://mpra.ub.uni-muenchen.de/49344/