auxiliary
sentence-ending particle indicating speculation, volition, or invitation
Dialectal (Kantō, Tōhoku) equivalent of だろう or う/よう. Used at the end of sentences to express conjecture, will, or suggestion. Informal and regional.
It'll probably rain tomorrow.
Let's go together.
auxiliary
Archaic auxiliary equivalent to modern べき. Expresses obligation or strong expectation. Not used in modern standard Japanese.
See also: べき
In old texts, 行くべい was used to mean 'should go'.
Archaic kanji form; not used in contemporary Japanese.
Derived from the classical auxiliary べし. The form べい is a dialectal and archaic variant, with the dialectal use surviving in Kantō and Tōhoku regions.