Should papers try to be self-contained?
There is no hard and fast rule on whether to include calculations in papers that have appeared in other papers. It is a judgment call on the part of the author. For my papers, I have sometimes included these equations (either in the main body of the paper or in the appendix) sometimes I have omitted them and directed the reader to the bibliography, and sometimes I have just provided a brief sketch of the argument.

The reason to include them is because sometimes they are convenient for the reader. The main reason to exclude them are because they detract from the focus of the paper. As an extreme example, if your important new ideas in a paper take up 3-4 pages, it is strange to include 50 pages of previously published calculations, say, even if it is in an Appendix. It makes it harder for me as a reader to understand exactly what is the main point of your paper, and I might get the impression that the authors are adding fluff to make their contribution seem more important than it is. You want to keep your novel, important ideas at the forefront of your paper.

And don't discount the page length: even if they are no explicit page limits in a journal, you generally want to convey your idea in as few pages as possible. First of all, is the possibility that potential readers might be discouraged from reading your paper if it seems too long. Secondly, journals do hold longer articles to higher standards. When I was submitting to the top ranked journal in my field (which had no explicit page limits) we were told by a senior professor that our idea was worth publishing there if we could keep it under 30 pages, and probably not worth publishing there if it hit 40. In other words, there was a sense where our idea was not worth wasting 40 pages worth of someone's time, although it was worth wasting 30 pages worth of someone's time.

In summary, papers don't necessarily have to be self-contained, and how much to include previous work is a judgment call on the part of the author. I will add that as a student, it is probably best to defer to the advisor when making these judgment calls, as the advisor will be more familiar with the conventions and culture of your research area.