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Problem

I am learning general linear mixed models and have a lot to still learn. Consider the following model, using glmmPQL I have the following model:

model <- glmmPQL(fatigue ~ hr + temp + participant + zone, data = training_dataset, family = binomial, random = ~1 | ratings, correlation = corAR1(form = ~1 | ratings))

How can I represent this model using mathematical notation?

I understand that a general linear mixed model under binomial assumptions is defined as $\vec{y} = \vec{X}*\vec{B}$ where $y = log(\frac{p_i}{1-p_i})$. My confusion is how to define $\vec{X}$ here? For instance, I know we have the fixed effects hr, temp, participant, and zone . So something like $X = B_0 + hr*B_1 + temp*B_2 + participant*B_3 + zone*B_4 + ???$ Where $???$ is my random effect, AR, and error term. I don't know how to describe this using mathematical notation.

A bonus question is, what is an excellent textbook on general linear mixed models, partial quasi-likelihood, and to learn more about addressing serial correlation like we find in glmmPQL ? I want to understand the theory behind glmmPQL deeply and would appreciate advice on how to accomplish this. I am very motivated to improve beyond my current ignorance, but believe I cannot do this without your kind and much appreciated guidance given the above.

Thank you for your patience and consideration in reading my question. I treasure this great community and the time you all take to gently improve each other.