My internal thesaurus seems to have a weak point and I don't know what search terms to enter in an on-line thesaurus for this one:
Is there a short, preferably monosyllabic, verb that means "to be absent"?
Less important for my present purposes but possibly also of some use would be one that means "to be present".
PS: Some commenters have asked for examples of how I want to use these words. Note that I have in mind short intransitive verbs, not adverbs. Two standard trigonometric identities for the sine and cosine of the sum of infinitely many terms express those as a sum of products. I want two write something along these line:
Each term on the right has finitely many sine factors and cofinitely many cosine factors. (That the prefix "co-" in "cosine" appears or fails to appear with the same prefix in "cofinite" is dumb luck, but useful as an aid to memory.)
"Appears" might serve for "to be present", but I prefer a monosyllable, and I think "with" doesn't quite fit as this stands but might fit better if a single word rather than "fails to appear" were used.