Kernel of GLM Log-Likelihood

In Agresti's Foundations of Generalized Linear Models, it states that the kernel of the log-likelihood function of a distribution in the exponential family is simply
sum(y_i*theta_i), but I'm confused as to why c(y_i,phi) is not included, as this is also a function of the range.

Basically, I am wondering why the orange squared part is not part of the kernel along with the pink square. Can someone help, please? Thank you.



Active Member
id guess because the orange box is not function of theta? so a sort of sufficiency thinger happening, ie when take derivative wrt theta, c term is 0.