K-finite

In mathematics, particularly in the context of algebra and representation theory, the term "K-finite" usually refers to elements in a representation (or module) of a group or algebra that have a certain finiteness property related to a subgroup \( K \). For example, in the representation theory of Lie groups, a representation is said to be K-finite if every vector in the representation space can be approximated by finite sums of vectors transformed by elements of a compact subgroup \( K \).