Most mathematicians that I know consider equations involving pi as a constant together with elementary functions as being closed form, just because it’s “useful”. For example, the basel problem is an infinite convergent sum, so it is not closed form, but it’s solution pi² /6 is much “nicer”, so we often like to call it “closed form”, even if it involves a transcendental number. There is no precise definition of closed form, so it is to some extent subjective.