A homogeneous linear recurrence relation with constant coecients is extended to the case in which the relevant quantities are not necessarily commutative with each other. Two kinds of its generating functions are explicitly given, and a relation between them is established. This result is essentially nothing but the reduction to a common (symmetric) denominator for a sum of fractions of non-commutative quantities.
Cite this article
Noboru Nakanishi, Quantum Recurrence Relation and Its Generating Functions. Publ. Res. Inst. Math. Sci. 49 (2013), no. 1, pp. 177–188