But would you agree that this definition is not universal?
math_04 gave a different definition:
The second sentence defines "religious behavior" as religiously motivated behavior and not behavior congruent to religious people. I don't think there's any ambiguity here.
"the expression for the logarithmic integral"
While there is an asymptotic expansion for the logarithmic integral of the form you propose it is not convergent. It is only a good representation of li(x) for a certain number of terms depending on x.
Other series for li(x) that do converge are...